# TRANSPORT AND TURBULENCE

D. R. Baker^2^, G. Bateman^3^, M. Beer^7^, A. Boozer^1^, B.E.
Chapman^13^, J. DeGroot^14^, W.Dorland^10^, E. Doyle^15^, P.
Efthimion^7^, C. Greenfield^2^, M. Greenwald^5^, G.W. Hammett^7^, B.
Hooper^4^, J. Kesner^5^, M.W. Kissick^15^, J-N. LeBoeuf^15^, Z. Lin^7^,
G. McKee^13^, D. Newman^9^, J. Sarff^13^, G. Staebler^2^, L.
Steinhauer^12^, E. Synakowski^7^, P. Terry^13^, D. Thomas^2^, R.
Town^8^, A. Ware^11^[^1]

^1^Columbia, ^2^General Atomics, ^3^Lehigh U., ^4^LLNL, ^5^MIT, ^6^ORNL,
^7^PPPL, ^8^Rochester, ^9^U. Alaska, ^10^U. Md., ^11^U. Mt., ^12^U.
Washington, ^13^UW-Madison, ^14^UC Davis, ^15^UCLA

# I[ntroduction]{.smallcaps}

This report is a summary of discussions held in the transport and
turbulence breakout subgroups of the Magnetic Confinement Concepts
Working Group (which met in the mornings) and the Plasma Sciences
Working Group (which met in the afternoons). It was the judgement of the
convenors of these groups, that a combined report was appropriate
considering the overlap in subject matter and membership of the two
groups. The report is organized to cover the most general topics first,
then to move on to more specific topics. IFE and basic processes were
primarily the focus of the Plasma Science group, while discussion of
specific MFE concepts was carried out in the Magnetic Concepts
breakouts. The substantial topic of MFE overarching issues was covered
extensively in both sets of sessions.

A strong consensus emerged in support of a physics program to understand
and control transport. The priority would be a program to develop a
science based predictive capability for transport, a program which would
benefit from a strong computational initiative but which is **not** to
be understood as simply a computational task. It was agreed that this
goal could only be achieved by the close interaction of experiment,
computation, and theory.

In the Transport and Turbulence Science Subgroup, there were 5 overview
talks at the beginning to help generate discussion, two on MFE (Jim
Drake and Ed Synakowski), and three on IFE (W. Kruer, J.P. Matte, S.
Glenzer). There were 15-20 shorter contributed talks (listed at the end
of this Transport and Turbulence summary) throughout the first week,
with lots of discussion after each talk. The two transport groups
independently prepared viewgraph summaries of their discussion, which
were incorporated in the MFE Concepts and the Plasma Science summary
talks (on record at
[www.ap.columbia.edu/fusion/snowmass/WG_summaries.html](http://www.ap.columbia.edu/fusion/snowmass/WG_summaries.html)
.)

The Turbulence and Transport Science Subgroup came to a general
agreement on 3 main goals:

Goal 1: Comprehensive transport models

Goal 1a: Pursue the challenging, yet realistic goal of developing
comprehensive predictive transport models, based on physically
reasonable assumptions and well-tested against experiments.

Goal 1b: Detailed Experiment/Theory Comparisons

Goal 2. Develop tools and understanding for control of transport and
transport barriers

Goal 3: Improved IFE heat transport models, and better understanding of
Fast Ignition Physics.

The MFE Transport subgroup reviewed issues for each concept in
discussions led by researchers in the field (Tokamaks-C. Greenfield,
ST-P. Efthimion, Stellarators-A. Boozer, ET-M. Kissick, RFP-B. Chapman,
FRC-L. Steinhauer, Spheromak-B. Hooper, Dipoles-J. Kesner). Common
issues were identified and were summarized:

-   Need for science-based predictive capability for transport including
    density limits.

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-   While empiricism has been useful, it can only take us so far

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-   Special requirements: particle and impurity transport, electron
    thermal transport, neoclassical transport, dynamics

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-   Need to control turbulence and transport barriers

The following sections describes these transport issues and goals in
more detail.

# U[nderstanding the]{.smallcaps} B[asic]{.smallcaps} P[hysics of]{.smallcaps} T[ransport]{.smallcaps}

Understanding turbulence and turbulent transport is one of the great
unsolved problems of physics, predating the revolutions in quantum
mechanics, relativity, and other areas that ushered in 20th century
physics. It is of fundamental importance in fluid mechanics and
applications thereof, atmospheric and oceanic sciences, astrophysics,
and plasma physics; and represents an important area within both
statistical physics and the rapidly developing field of nonlinear
dynamics. Turbulence is a natural and robust byproduct of the large
gradients that are required to maintain fusion plasmas far from
equilibrium. Because the transport driven by turbulence seeks to restore
the plasma to equilibrium, it is generally deleterious to the
maintenance of fusion conditions. An exception is turbulence in the
scrape-off-layer that is useful in spreading out the power to the
divertor plate. Intelligently dealing with the turbulence problem in
fusion, under the numerous constraints imposed by heating, current
drive, steady state operation, profile control, ash removal, burn
control, economic feasibility etc., requires significant advances in the
understanding and control of turbulence and will, because of common
dynamics, benefit the other fields mentioned above. Furthermore, the
potential impact is expanding because fusion turbulence studies are
moving from analyses of linear instabilities and the saturation of
simplified nonlinear systems to studies that treat plasma turbulence as
a globally distributed, bounded flow, and probe for universal features.
Under this trend, the problems of fusion turbulence are increasingly
relevant to many classical fluid dynamics problems such as turbulent
boundary flows and turbulent shear flows. Fusion turbulence studies are
also beginning to consider the effects of magnetic as well as
electrostatic turbulence, which is crucial at high plasma pressure (β)
and important in self-organized plasmas such as the RFP and spheromak,
making it more relevant to astrophysical and space plasmas.

Examples of fusion plasma turbulence problems with these connections are
so numerous that only a partial listing can be attempted here. They
include issues that deal with nonlocality, such as the relationship
between global scales and local instability, what governs whether
transport reflects global or local scaling, the effect of the plasma
boundary on edge and core turbulence and its impact on mean spatial
profiles, and the effect of small scale turbulence on large scales and
the mean state through turbulent dynamo and flow drive processes. They
include issues that deal with flows, such as the relationship of flow
shear-induced transport barriers in fusion plasmas to atmospheric
transport barriers, the relationship of Reynolds stress driven flows in
the atmosphere to the shear flows of fusion transport barriers, the role
of shear suppression in wall flows and turbulent boundary layers, and
the physics of zonal flows. They include issues that deal with closure
in turbulent systems and intermittent behavior, such as the role of
subgrid scales on turbulence and their appropriate treatment, the role
of spatial and temporal intermittency in turbulence and transport and
its origin and proper treatment, and what types of fluctuations
(collective resonances, clumps, holes, vortices, convective cells, zonal
flows, eigenmodes of nonlinear instabilities, etc.) lead to the most
advantageous decomposition of the turbulent spectrum. They also include
issues that deal with dynamical processes, such as the role of nonlinear
instability, the origin of residual fluctuations and transport in
transport barriers, and the physics of coupled fluctuations and free
energy sources.

A successful attack on the difficult problem of turbulence in fusion
requires a recognition of its relationship to the general fundamental
problem of turbulence, both to exploit advances made in related fields,
and to foster support for fusion because of the contributions it has
made and will make to the understanding of turbulence. Successes within
the general field of turbulence suggest an approach to solving the
fusion problem that incorporates the following elements.

1\. In experiment

a\. Carry out experiments on existing devices that are designed to
optimize comparison with appropriate theory.

b\. Develop new diagnostics to provide a better picture of turbulence in
fusion devices and to address issues such as fluctuation structure and
intermittency

c\. Develop new analysis techniques for existing and new diagnostics
that relate more directly to basic processes in turbulence, and
therefore to basic elements of theory.

d\. Develop specialized plasma devices to answer specific questions in
turbulence that are not answered with existing devices.

A plan that establishes an appropriate balance between these elements
should be developed.

2\. In theory / simulation

a\. Understand the basic dynamics of the complex turbulent systems of
fusion experiments. This includes analysis of pieces of complex
simulation codes, e.g., individual nonlinearities, studies of scaling
properties, and analytic and computational studies of simplified models.

b\. Understand how the basic elements integrate in the full system, and
therefore what processes govern behavior of the full system under a
range of relevant conditions.

c\. Develop a range of appropriate models that synthesize behavior of
the full system. Models that range from simplified paradigms with
correct qualitative behavior to realistic simulations with predictive
capability should be developed and employed. For example, simplified
models that capture key physics of nonlinear instabilities could be fit
to direct nonlinear simulations, and then used as reduced models in
transport codes. Effective subgrid turbulence models could help increase
speed of nonlinear simulations.

d\. Execution of these steps should employ a synergistic combination of
analytic theory, simulation, and experiments, utilizing meaningful
comparisons and correlated development.

# I[nertial]{.smallcaps} F[usion]{.smallcaps} E[nergy]{.smallcaps} I[ssues and]{.smallcaps} O[pportunities]{.smallcaps}

# Introduction

There are currently two main approaches for inertial fusion energy (IFE)
target designs: direct and indirect drive. A comprehensive review of IFE
target physics issues can be found in References 1 and 2. In the
indirect-drive approach, energy from lasers, or heavy-ion beams, is
converted in a *hohlraum* into x rays. These x rays are transported from
the *hohlraum* walls to the implosion capsule, where they are absorbed
by the *ablator*. The ablator heats and expands, driving the remainder
of the shell inward thereby compressing the DT fuel. In the direct-drive
approach the laser is incident directly on the imploding capsule. In
both approaches the final DT-fuel configuration consists of a
high-temperature *hot spot* that ignites and starts a propagating burn
wave through the high-density *main fuel layer*, which surrounds the hot
spot. For robust high-gain designs, it is vitally important to assemble
the high-temperature hot spot and the cold, dense main fuel layer
accurately.

The fast-ignitor approach (3) relies on a somewhat different ignition
scheme than conventional direct or indirect drive. First, lasers,
heavy-ion beams, or a Z-pinch is used to assemble a high-density DT fuel
without the central hot-spot region. Then a high-intensity short-pulse
laser impinges on the stagnated core to generate a hot spot and thus
initiates the burn wave through the fuel.

**Thermal Transport in IFE**

Preheat of the fuel will increase the pressure of the fuel and thus make
the target harder to compress. The amount of preheat can be quantified
in terms of the *adiabat* *α* of the implosion. The adiabat is defined
as the ratio of the fuel specific energy to the Fermi degenerate
specific energy. It can be shown that the gain *G* of the target scales
as α^-3/5^. Having a detailed model of thermal transport is therefore
important in IFE target designs. J-P Matte presented an overview of the
status of IFE transport simulation and theory. The majority of the
predictive simulation codes used in IFE target design work rely on
flux-limited Spitzer thermal transport. In this approach the classical
Spitzer heat flow is limited to some fraction *f* of the free-streaming
heat flow (the maximum possible heat flow.) The value of the flux
limiter has been established by comparing experiments to hydrodynamic
simulation codes. For current direct-drive ICF implosions *f*=0.06. The
next level of complexity in simulation codes solves the Fokker-Planck
(FP) equation for the electrons and assumes fluid ions. These codes have
shown good agreement with experimental data but typically have less
physics modules than hydrocodes and mainly have only one spatial
dimension (compared to the two, or three dimensions used in hydrocodes).
In typical ICF plasmas the agreement between FP codes and flux-limited
Spitzer hydrocodes is very good, apart from the existence of a small
preheat "foot" ahead of the main heat front in the FP case. This foot
could preheat the fuel (increasing the adiabat and reducing the target
gain) and reduce the Rayleigh-Taylor (RT) growth rate at the ablation
surface. Flux-limited Spitzer hydrocodes show good agreement with RT
growth rates, which implies that the effect of the foot on the target is
swamped by the physics effects (non-LTE radiation transport, real EOS)
included in the hydrocodes, but absent from FP codes. An intermediate
approach involves the construction of a convolution formula for heat
flow. These models have proven useful but require validation with FP
codes when used in new regimes. Magnetic fields are not included in FP
codes. Many hydrocodes have magnetic fields, but the computational
expense of including them means that the hydrocodes are routinely run
without magnetic fields. S H Glenzer presented a review of transport
experiments. These experiments use a 4 beam to perform Thomson
scattering measurements. In hohlraums the temperature measurements are
in good agreement with LASNEX simulations when magnetic fields were
included (4); however, inclusion of magnetic fields resulted in steep
density gradients. These steep gradients could increase light
refraction, resulting in decreased symmetry. Such gradients will detune
SRS and lead to a smaller reflectivity than calculated for a homogeneous
hohlraum plasma. More calculations and experiments are required. J
Hammer reviewed the LASNEX simulations, which showed the potential
importance of magnetic fields on laser-driven IFE hohlraums.

To summarize, current indirect-drive experiments are adequately modeled
using flux-limited Spitzer thermal transport and self-generated magnetic
fields. However, IFE hohlraums may have higher temperatures, and
nonlocal transport will be more important. Direct-drive experiments are
well modeled with flux-limited Spitzer thermal transport. However,
direct drive targets are more sensitive to hot-electron transport,
therefore controlling the source of hot electrons and accurately
modeling their transport are important. The availability of massively
parallel architecture computers opens the possibility to incorporate
more-sophisticated heat transport models into predictive simulation
codes. We therefore have an opportunity to improve our heat transport
modeling, which will increase our confidence in achieving laser-driven
IFE.

**Laser Plasma Instabilities and Turbulence in IFE**

The interaction physics between the laser and the plasma is a vital
element of laser-driven IFE. The laser energy must efficiently couple to
the target without the generation of hot electrons and with excellent
spatial and temporal control. W L Kruer presented a review of the
potential instabilities that may be excited by the interaction of the
laser with the coronal plasma. These include the ion-acoustic, Raman
(SRS), Brillouin (SBS), and two-plasmon-decay instabilities and the
potential for the filamentation of the laser beam. These nonlinear
processes place constraints on the overall IFE target performance.
Calculations show that current direct-drive IFE target designs are only
susceptible to the two-plasmon-decay instability. This instability can
produce hot electrons that can preheat the fuel. Experiments on OMEGA
with NIF direct-drive density and temperature scale lengths have shown
very low levels of SRS and SBS backscatter (5). Control of nonlinear
processes in laser-driven hohlraums is a greater challenge, but has been
successfully demonstrated in Nova experiments by the use of laser-beam
smoothing (SSD). Plasmas generated on Nova have attempted to simulate
NIF conditions and have demonstrated adequate control of instabilities;
however, the integrated experimental test awaits the completion of the
NIF. Kruer reviewed the theoretical tools used to investigate these
phenomena. These range from the 3-D particle-in-a-cell (PIC) codes to 2-
and 3-D reduced models (such as F3D). With the rapid advances in
computer power, more-realistic (larger system sizes for longer times)
simulations have become possible. J C Fernandez reviewed Los Alamos
Trident experiments on saturation mechanisms for SRS. He pointed out
that NIF-hohlraum conditions could result in high laser plasma
instability levels. This result depends on filamentation and saturation
mechanisms for SRS. Well diagnosed Trident experiments that model a
laser hot spot in a NIF hohlraum will help resolve this important issue.

In summary, current experiments with 3 smoothed beams that model
NIF-scale plasmas have low laser-plasma instability levels, although
some uncertainty exists. Some uncertainties also exist for recent
high-gain designs. Little work on the effect of 2 beams on laser-plasma
instabilities has been done. The use of 2 beams increases the damage
thresholds of final optics and increases the efficiency of the laser.
With the availability of high-performance parallel computers an
excellent opportunity exists to develop an integrated predictive model
for incorporation in IFE target-design codes.

**Fast Ignitor Transport and Turbulence Issues**

The fast ignitor concept is at an earlier stage of development than the
main-line direct- and indirect-drive approaches outlined in the
preceding sections. Thus there are greater uncertainties in the physics
modeling; in particular the main issues facing the fast ignitor concept
are in the area of transport and turbulence. M Tabak presented an
overview of the fast ignitor concept and the theoretical models that
have been used. M H Key reviewed fast ignitor experiments performed to
date. The key issues are (1) transport of the short-pulse,
high-intensity laser through the underdense plasma to the critical
surface; (2) efficient coupling of the laser light to hot electrons; and
(3) transport of the hot electrons to the high-density compressed-fuel
"ignition" region. The 2-D PIC codes are used to study the propagation
of the laser through the underdense corona, where filamentation and
other nonlinear processes may occur. To theoretically study the
transport of the hot electrons through the overdense material, a range
of codes (from LASNEX with magnetic fields to GAPH, a PIC code for hot
electrons and a fluid background and similar models developed outside
the USA) have been used. The forward currents in this region can reach
10^5^ Alfven currents, so magnetic fields, current, and charge
neutralization will be important. Experiments using gold foils buried at
various depths in plastic targets have shown an annular x-ray emission
pattern that persists in diameter at depths of 15 - 100 *μ*m. This
suggests collimated electron transport over relatively large distances
in qualitative agreement with theoretical predictions.

In summary, the fast ignitor concept offers the potential for
significantly higher gains (\~5 times that of conventional IFE), but the
transport of the hot electrons to the cold, dense fuel requires more
theoretical and experimental research. This will entail the further
development of hybrid PIC/fluid codes and access to a petawatt-class
laser facility.

**References:**

1\. J. D. Lindl, "Inertial Confinement Fusion"(AIP Press: an imprint of
Springer-Verlag New York Inc., New York, 1998).

2\. S. E. Bodner, D. G. Colombant, J. H. Gardner, R. H. Lemberg, S. P.
Obenschain, L. Phillips, A. J. Schmitt, J. D. Sethian, R. L. McCrory, W.
Seka, C. P. Verdon, J. P. Knauer, B. B. Afeyan, and H. T. Powell, Phys.
Plasmas **5**, 1901 (1998).

3\. M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks, J.
Woodworth, E. M. Campbell, and M. D. Perry, Phys. Plasmas **1**, 1626
(1994).

4\. S. H. Glenzer, W. E. Alley, K. G. Estabrook, J. S. De Groot, M. G.
Haines, J.H Hammer, J. P. Jadaud, B. J. MacGowan, J. D. Moody, W.
Rozmus, L.J. Suter, T. L Weiland, and E. A. Williams, Phys. Plasmas
**6**, 2117 (1999).

5\. S. P. Regan, D. K. Bradley, J. J. Carroll III, A. V. Chirokikh, R.
S. Craxton, R. P. Drake, D. D. Meyerhofer, W. Seka, R. W. Short, A.
Simon, R. P. J. Town, and B. Yaakobi, Phys. Plasmas 6, 2072 (1999).

# MFE - O[verarching]{.smallcaps} I[ssues]{.smallcaps}

# 

# Introduction

During discussions of specific MFE concepts, a broad set of issues arose
repeatedly. These same issues were raised by speakers and within
discussions in the sessions of the Plasma Science/Transport group. This
convergence suggests that there is indeed a substantial overlap in the
interests of the entire community. It seems likely that, at least with
these areas, progress made in developing an understanding of transport
in one concept will be transferable to others.

There was general agreement that the overall priority should be the
development of a predictive capability based on a sound physics
base.[^2] The consensus was that this was the surest and most direct
route for future progress in understanding and controlling transport.
Empirical scalings (of such things as the global confinement, or the
power threshold for H-modes or internal transport barriers) have been
useful, but they have their limits and there are often significant
uncertainties in extrapolating them. While a predictive capability has
been a goal of researchers in the field and a focus of the Transport
Task Force, the group felt that it has not been pursued vigorously as a
programmatic goal within MFE. Resources would have to be applied - we
are still not measuring many of the quantities that are critical to
understanding turbulent transport, diagnostic access and run time need
to be made available, and advanced computational tools need to be
further developed and exploited. An important component of this approach
is the close interaction of experiment, computation, and theory.

There was substantial agreement on what the components of a physics
based transport program would be and on what direction we need to move.
Clearly more physics needs to be put into the existing computer codes;
our groups tried to enumerate and prioritize the opportunities. New
diagnostics need to be developed and deployed, innovations must be
explored and exploited. We must expand our efforts to control turbulent
transport and profiles. Perhaps most importantly, we must increase the
systematic comparisons between theory, computation, and experiments.
Improved coordination will be essential; theorist must look to
experiments to help guide calculations and experimentalists must look to
theory to help determine what to measure.

# 

# Develop Comprehensive 3-D Turbulence Simulations

A high priority goal supported in the discussions was the development of
comprehensive predictive transport models based on physically reasonable
assumptions. All computer simulations make approximations of the real
world in various ways, but the growth of computer power and the advances
in physics understanding and algorithms have been sufficiently large
that it is believed that fairly realistic 3-D nonlinear simulations of
plasma turbulence are becoming possible. Detailed comparisons of such
simulations with experiments would help validate the simulations and
provide insight into the complicated dynamics of turbulence. Such
simulations could improve confidence in the extrapolations to reactor
scales, and could help optimize the design of fusion reactors. This goal
is perceived as challenging but achievable, and will require a serious
effort by a significant number of people. It will require not just
advances in computer simulations and use of the latest massively
parallel computers but also detailed tests against experiments. There
are two parts to this goal: the development of realistic 3-D nonlinear
simulations of plasma turbulence (in this section), and their interface
with large integrated transport codes (in the next section).

Moore\'s Law is the observation that computer power has been doubling
approximately every 1.5 years. This corresponds to a factor of 100
improvement every 10 years, making simulations practical now that were
unthinkable just 10-20 years ago. Simulations have also benefited from
advances in theoretical techniques and algorithms, guided by
experimental evidence indicating the relevant range of time and spatial
scales on which to focus. For example, many orders of magnitude
improvement in computational speed have resulted from the development of
the nonlinear gyrokinetic equation (which analytically removes
high-frequency gyromotion from the Vlasov/Boltzmann equation while
retaining nonlinear effects), the delta-f particle simulation method,
efficient coordinate systems, and fluid closure approximations.
Turbulence in plasmas shares some characteristics with regular fluid
turbulence, but one of the unique features is the existence of
wave-particle resonance effects which provides instability in some
ranges of wavenumber k and damping in other ranges of k. At least for
certain types of plasma turbulence, these wave-particle resonances and
other damping processes cause the range of spatial scales that need to
be resolved for a direct numerical simulation to be less severe than for
regular fluid turbulence.

Computer simulations in the 1980\'s focussed primarily on 2-D
simulations, though there were some initial 3-D simulations at modest
resolution in simplified systems. Recognizing the opportunity for fusion
research to make effective use of the new computational power that was
becoming available, the Numerical Tokamak Turbulence Project (NTTP) was
selected in 1992 as one of the Grand Challenge computational projects
supported by DOE's part of the High Performance Computing and
Communications Program. The 1990\'s saw the development of higher
resolution 3D simulations in realistic tokamak geometry, most of them
part of the NTTP. These toroidal simulations focussed primarily on
electrostatic adiabatic-electron gyrokinetic and gyrofluid simulations
of core ion turbulence, or on electromagnetic collisional fluid
simulations of edge turbulence. \[The electrostatic simulations allowed
ExB fluctuations but neglected magnetic fluctuations.\] These
simulations have had a significant measure of success, producing
fluctuation spectra that are qualitatively similar to observations and
leading to transport models that can follow many experimental trends
(see the next section on transport modeling). These simulations have
also helped build qualitative insight into transport barriers and the
important role of ExB zonal flows. However, it is clear that additional
physics needs to be added to the simulation codes to make them
sufficiently complete and robust for predictions over the full minor
radius in a wider range of parameter regimes. Also, previous simulations
have tended to focus on primarily the ion thermal transport (though some
work has included trapped electrons or collisional fluid electrons which
can drive electron thermal and particle transport), while simulations
are needed of all transport channels (electron and ion thermal flux,
electron and impurity particle flux, momentum flux). The advances that
were made in the 1990's involved a lot of work by many people in
developing complicated computer programs with more complete physics
models, developing and testing algorithms and theoretical methods,
cross-checking codes against each other, and comparing code results with
experiments. Much of this work was part of the Numerical Tokamak
Turbulence Project, which was important in coordinating and focusing
these group efforts, in funding some of the work, and in providing
access to a large amount of computer time on the latest generation of
massively parallel computers. Building on this work and achieving the
level of realism set out as a goal here will likewise require a
significant effort by many people.

One of the main challenges in the near future is to develop simulations
with full electromagnetic fluctuations including kinetic effects and
electron dynamics, and to fully explore the resulting turbulence
characteristics. This is challenging because including magnetic
fluctuations introduces Alfven waves that require reducing the time step
in the simulations by a factor of 1/sqrt(β)\~ 10. If full electron
dynamics are kept, the time step must be reduced relative to
electrostatic simulations by a factor of sqrt(m~i~/m~e~) \~ 60, unless
analytic orderings or implicit numerical methods are used to avoid these
fast electron transit time scales.

While the electrostatic approximation has been useful in low beta
tokamak plasmas, fully electromagnetic simulations are important for
higher beta tokamaks and Advanced Tokamak regimes, and are needed to be
able to simulate alternate concepts such as ST\'s, RFP\'s, high-beta
stellarators, etc. Electromagnetic effects and electron dynamics are
naturally coupled, and such simulations could also predict all of the
transport channels, including particle transport. There is a wealth of
experimental evidence on the scaling of particle transport, including
puzzling observations of particle pinches in some regimes, that would
provide a valuable test of such simulations. The ability to predict
particle transport is important because the fusion power improves
significantly by density peaking or by increasing the total density (so
a physical understanding the empirical density limit is important), and
the details of the density profile near the edge could have a
significant impact on the height of the H-mode temperature pedestal and
on the operation of the divertor.

Because of the importance of electromagnetic effects, there has been
some recent work on including them in some simulations. Also, edge
turbulence simulations using collisional Braginskii equations have
included magnetic fluctuations during the past several years, though
this is somewhat more manageable because the Alfven frequency, the
electron transit frequency, and the drift wave frequency are all
comparable in the edge.

In addition to the electromagnetic goal, another main goal is the study
of the interaction of disparate scales in plasma turbulence. Several
types of effects are grouped under this goal. Full torus and annular
wedge simulations (and perhaps extended versions of flux-tube
simulations) will be useful for studying the effects of the
equilibrium-scale radial variation of parameters such as ω~\*~(r) or
η~i~(r) on the small-scale turbulence. Sometimes such effects may be
similar to sheared flows and may reduce the turbulence level. These
effects may also lead to a certain degree of radial propagation and
nonlocality in the turbulence, or to avalanches or SOC-types of
dynamics. These types of effects may be more important near the plasma
edge with its sharp gradients. Turbulence-generated zonal ExB flows
(poloidal flows with m=n=0) play a major role in the turbulence dynamics
and need to be understood better. The formation of transport barriers
and the dynamics of ELMs may involve physics that occurs on a wide range
of time scales, and so may involve running turbulence simulations for a
very long time to follow the slower evolution of the m=n=0 components.
In some edge simulations it may be important to include some atomic
physics and sources and sinks or the interaction with the
scrape-off-layer. Another disparate scale issue is the possible
nonlinear interaction of ETG and ITG turbulence.

There are a range of computational techniques in use in present plasma
turbulence simulations, including direct full torus gyrokinetic particle
simulations, and reduced-volume flux-tube simulations using gyrokinetic
particles or grids, or gyrofluid or collisional Braginskii fluid
equations. Each of these has strengths for focusing on certain types of
problems, and the range of problems being investigated is sufficiently
difficult that this multiplicity of approaches is helpful. Comparing
different simulations also helps to build insight.

Although there is no substitute for real experiments, computer
simulations are easier to diagnose than real plasmas, so they can help
develop fundamental understanding of the underlying nonlinear dynamics
by detailed comparisons with various analytic theories. Simulations can
also help extend the value of experimental measurements by helping to
unfold multiple processes that may be affecting a measurement. A
particularly fruitful area of experiment/simulation comparisons should
be measurements of the spectra in frequency and in space (1D to 3D).
While comparisons of measured and predicted temperature and density
profiles will continue to be useful, comparisons of the fluctuation
spectra provides a more direct link into the underlying turbulence
processes.

# Predictive Transport Modeling Issues

The objective of predictive transport modeling is to understand the
plasma temperature, density, current, and momentum profiles measured in
previous experiments and to predict them in future experiments and
planned devices. Large predictive transport modeling computer codes,
such as BALDUR, ONETWO, TSC, and WHIST, use physics-based or empirical
models to compute all the sources, sinks, fluxes, large scale
instabilities, and boundary conditions needed to predict the plasma
profiles. Much of the input data needed to run these codes are similar
to the controls that experimentalists use to run experiments. Detailed
comparisons with experimental data are then used to test models and to
improve our understanding of transport physics.

There are currently at least four theory-based transport models that
have an RMS scatter of only 15-30 % compared with experimental data over
a wide range of conditions. These transport models are the Multi-Mode
model (MMM) developed by Singer, Bateman, Kinsey and Kritz; IFS/PPPL
developed by Kotschenreuther, Dorland, Hammett and Beer; GLF23 developed
by Waltz *et al*.; and CDBM developed by Itoh, Itoh, and Fukayama. The
best of the empirical transport models also match experimental data
equally well. However, fusion power scales as the square of the
temperature, and the feedback of the alpha heating at high gain further
increases the sensitivity to transport, so even higher accuracy is
needed. Also, there are outliers in the experiment/prediction
comparisons, i.e. parameter regimes where the models do not do so well,
and it is clear that further improvements in the models are needed.

Six issues have been identified for predictive transport modeling
research during the next 10 years:

\(1\) convergence of transport models for reliable extrapolation to
fusion reactors;

\(2\) reliable models for the plasma boundary need to be implemented
within integrated modeling codes;

\(3\) accurate models are needed for momentum transport and flow shear
effects (leading to transport barriers);

\(4\) improved models are needed for sawtooth oscillations and Edge
Localized Modes (ELMs);

\(5\) high quality computer modules need to be shared among transport
modeling codes

\(6\) the practicality of running turbulence simulations within
integrated transport modeling codes.

*convergence of transport models* Different transport models
representing different approximations to the same physics match most of
the steady-state experimental data reasonably well, but predict very
different fusion reactor performance. The Multi-Mode and CDBM models
predict that ITER will ignite easily \-\-- even with L-mode boundary
conditions at high enough density \-\-- while the IFS/PPPL and GLF23
models predict that ITER will not ignite unless the H-mode pedestal
temperature is very high. Further experimental tests which could help to
better distinguish between different transport models include
time-dependent pulse propagation experiments, and controlled scans of
rotation, plasma shaping, etc. Developing more accurate physics-based
transport models based on more complete 3D turbulence simulations (such
as described in the previous section) would also be helpful, and
comparisons of such simulations with measured fluctuation spectra would
provide more direct tests of the causal links in the turbulence.
Non-linear gyro-*fluid* simulations of turbulence, which formed the
foundation of the IFS/PPPL and GLF23 transport models, have been found
to give too much transport compared with non-linear gyro-*kinetic*
simulations in the collisionless adiabatic-electron limit. Work is
needed to bring the gyrofluid simulations into agreement with the
corresponding non-linear gyrokinetic simulations, including the effects
of collisions and non-adiabatic electrons which may reduce the
differences, and to correct the transport models which were based on the
gyrofluid simulations.

In order to develop better transport models during the next ten years,
we need to implement more physics in the non-linear gyro-kinetic
turbulence simulations \-\-- particularly electromagnetic effects and
more detailed electron dynamics physics. Many more non-linear
gyro-kinetic turbulence simulations then need to be carried out over a
wide range of plasma parameters.

*Predicting boundary conditions.* most transport modeling codes use
experimentally measured temperatures and densities for their boundary
conditions, and the predictions of most modern transport models are very
sensitive to these boundary conditions. Computed boundary conditions are
needed for completely self-consistent predictions of plasma profiles.
There are separate, well-developed computer codes that model the 2-D
scrape-off layer at the edge of plasmas that need to be merged together
with the core integrated modeling transport codes. In addition, reliable
models need to be developed to predict the height of the pedestal that
forms at the edge of H-mode plasmas, together with a model for the Edge
Localized Modes (ELMs) that periodically sweep this pedestal away.
Finally, more reliable edge turbulence models need to be developed for
more complete, self-consistent transport predictions from the edge to
the center of the plasma.

*self-consistent predictions for toroidal and poloidal momentum profiles
and a more accurate model for the effects of flow shear.* There are
currently three core transport models that compute the transport of
momentum \-\-- Houlberg et.al.'s neoclassical NCLASS model, Ernst'
neoclassical and anomalous TRV code, and the GLF23 model for anomalous
transport. These need to be implemented within integrated predictive
transport codes, along with computations of momentum sources and sinks,
to produce self-consistent predictions of the net momentum profiles as a
function of time and radius across the plasma (the TRV and GLF23 codes
accomplish this at present as postprocessors using other codes to
calculate the beam-driven toroidal torques). It may be necessary to
include models of turbulent-driven Reynold's stress poloidal torques in
some cases. In regions where the plasma momentum has strong gradients
(flow shear) it is known that transport is reduced and transport
barriers are formed. More accurate models are needed for these important
effects.

*improved models for sawtooth oscillations and Edge Localized Modes
(ELMs).* these large scale instabilities can have a large impact on
experiments and fusion reactors, because they periodically rearrange the
plasma profiles. We need a more reliable model for the frequency and
radial extent of these instabilities, and for their effect on fast ions.

*sharing modules in the National Transport Code Collaboration (NTCC)
Module Library*. Modules that are submitted to the NTCC Module Library
are refereed according to published standards. For example, modules must
include test cases, they must run correctly on different computers, they
must be well documented, and they must have a well isolated input and
output. Bringing computer modules up to these standards is expected to
make it easier to maintain the large integrated transport modeling
codes. Many more modules are needed in this library to build complete
integrated transport codes.

*running complete turbulence simulations within integrated transport
modeling codes.* This is motivated by the fact that transport is found
to be a complicated function of many plasma parameters (gradients,
geometry, ratios of temperatures and densities of different species, . .
.) and transport may be non-local. At first, reduced transport modules
that are fast enough to run inside of a large transport code would be
fit to comprehensive turbulence simulations. After a transport code
runs, the comprehensive turbulence simulations may be rerun in some
cases to cross check the results of the reduced transport modules. As
computers become faster and their memory becomes larger, we may be able
to run turbulence modules directly within large transport codes within
the next ten years. Initially, turbulence simulations would be run on
only a subset of time steps and radial points, and they could be used to
fine-tune the operating transport model on the fly. The objective would
be to produce more reliable predictive transport simulations based on
first-principles physics.

# Improve Experiment/Theory/Computational Comparison and Coordination

In order to further both the scientific goals of understanding
turbulence and transport in plasmas and the programmatic goal of
utilizing that understanding to control transport and make fusion a
practical energy source, an improved comparison between experiment,
theory and computation is needed. In order to achieve this goal,
improvements (or changes) are needed in all three areas. In the
experimental area, dedicated run time must be allocated for experiments
specifically designed to test aspects of the theory using relevant
diagnostics. This often will mean simply an improved utilization of
existing diagnostics in operating regimes thought to overlap with
modeling and theory capabilities. However, in some cases, development of
novel new diagnostics will be required to make measurements that can be
compared with theory and computation (e.g. localized short wavelength
fluctuation measurements for comparison with ETG and other theory
predictions). In the computational area, simulated diagnostics should be
"built" for more realistic comparison with experimental measurements.
The models should also be run for as wide a range of "reasonable"
parameters (that is, parameters which are both consistent with the
assumptions built into the model and in physically realizable regimes)
as possible. In the area of theory, experimentally verifiable
predictions should, when possible, be a goal. Coupled with the
individual efforts, enhanced analysis techniques are needed to
facilitate the actual comparisons. This is because all measures are not
equal in comparisons (e.g. different. models can give the same
fluctuation spectra and fluctuation mean etc). Very often it is in the
tails of the probability distribution functions (PDFs), the parts most
difficult to investigate, that the differences show up. Therefore, a
hierarchy of comparison techniques should be employed. These can
include; basic statistics (mean variance etc), spectra (frequency and k,
with long enough saturation regime), time evolving spectra (plasma
turbulence spectra are rarely steady stationary, wavelets can be
useful), bi-spectral techniques to infer growth rates (both linear and
nonlinear) nonlinear transfers etc, quantile-quantile (for non-normal
comparisons), correlation functions (auto and cross, spatial and local),
structure functions (to investigate intermittency etc), and R/S analysis
(to investigate system dynamics). All of these techniques can and should
also be used for inter-model comparisons, inter-experiment comparisons
(to help address the issue crosscuts) and innovative concept experiments
and true predictive theory-model comparisons as well as
computation-experiment comparisons.

Successful comparisons will form a basis for predictions of new regimes,
leading to

next step and capabilities.

# Diagnostic Improvements

A dramatic improvement in the understanding of the turbulent mechanisms
driving anomalously high levels of cross-field energy and particle
transport in magnetic confinement devices has been achieved during the
past decade. This accomplishment is due in large part to the combination
of theoretical simulations of turbulence, detailed profile measurements
of density and temperature, and the development of fluctuation
diagnostics to experimentally characterize the underlying turbulence.
Nevertheless, a great deal remains to be learned and the development of
more advanced fluctuation diagnostics, improvements in existing
diagnostics and implementation of profile and fluctuation diagnostics on
a greater variety of magnetic configurations will play a crucial role in
increasing our understanding of the basic physical principles, as well
as provide greater confidence in our predictive capabilities. Particular
issues to be addressed include turbulent mode identification, LH
transition physics, ExB shear dynamics, as well as broad ranging issues
including indications of the universality or self-organizing nature of
plasma turbulence across various magnetic configurations, and the
potential for stabilization in ST and ET devices.

It is desired to obtain fluctuation measurements of several plasma
quantities (n, Ti, Te, φ, B, v) over a wide range of wavelengths (0.5 \<
­k \< 50 cm-1) to most fully characterize turbulent driven transport
(Γ=\<nvr\>, q=\<nvT\>, \...). Existing fluctuation diagnostics are
focussed dominantly, though not exclusively, on the turbulent density
field and development has emphasized application to tokamaks. Examples
of such existing diagnostics include scattering (microwave,
far-infrared, CO2), (correlation) reflectometry (local ñ, Lc,r (radial
correlation length)), beam emission spectroscopy (local ñ, Lc,r Lc,θ),
Langmuir probes (local ñ,\~φ at edge/SOL), phase contrast imaging (ñ,
S(kr)), among others. In addition, electrostatic potential fluctuations
are measured with Heavy-Ion Beam Probes, through with limited
application. Electron temperature fluctuations can in principle be
obtained with correlation ECE, though this technique is under
development. Limited ion temperature fluctuation measurements have been
obtained using fast charge exchange recombination spectroscopy. Magnetic
fluctuations are crucial to understanding RFP (and perhaps other)
transport, and possibilities for measuring this include
cross-polarization scattering, though further demonstration is required.
These techniques have made valuable contributions, yet can all benefit
from improvements (e.g., temporal and spatial resolution,
signal-to-noise ratio). It is also noted that while the primary focus of
fluctuation diagnostics is for transport and turbulence studies, these
diagnostics have been applied to examination of MHD phenomena (e.g.,
TAE, NTM mode structure), and to measurements of RF mode-coupling
behavior, and so have a broader application within MFE research.

There is significant interest in obtaining two dimensional images of
turbulence. Turbulence in magnetically confined plasmas is fundamentally
quasi-2D (3D but very elongated along the magnetic field) in nature, and
simulations can now model the 3D nonlinear dynamics, while most
fluctuation measurements are 1D or point measurements. It is therefore
desired to provide comparable 2D measurements for visualization
applications as well as to more fully examine the nonlinear mode
coupling features. Some concepts under development or being considered
for 2D imaging of density fluctuations include edge/SOL Langmuir probe
arrays, imaging BES, laser induced fluorescence, reflectometry,
fluorescent plate imaging (cool plasmas)\....

Another key area in which to develop advanced diagnostics is higher-k
measurements. While ion transport appears to be fairly well understood
in tokamaks, knowledge of electron particle and energy transport remains
far more elusive. An area of intense theoretical and experimental study
is higher-k modes (e.g., ETG) that may be controlling electron thermal
transport in some regimes. As such, it is desired to develop high-k (k
\> ­5 cm-1) diagnostics for any and all plasma quantities. Possibilities
include high-k FIR scattering techniques.

Profile and fluctuation measurements are fairly well developed on the
tokamak, yet are required for other configurations. The existing methods
often suffer from either not being applicable to other configurations,
or simply being too expensive to deploy on smaller concept development
machines. Efforts should therefore be made to provide profile
diagnostics, required for transport studies, as cheaply as possible.
This might be accomplished by developing less expensive profile
measurement techniques, as well as by utilizing equipment from "retired"
machines, if applicable, to the maximum extent possible. Other options
may include more limited profile diagnostics: fewer channels, lower time
resolution. Similar issues apply to implementing fluctuation
measurements on such devices. Table 1 summarizes a list of existing
profile and fluctuation diagnostics and where they have been or could
reasonably be deployed.

We also note that it is desired to implement "simulated diagnostics" in
the various modeling codes so that nonlinear simulation results can be
directly compared with fluctuation measurements. This would involve
applying the finite spatial resolution and volume sampling, time
resolution, and providing lab-frame equivalent measurements
(incorporation of plasma rotation, radial electric field effects). This
topic is addressed in more detail in the experiment/theory comparison
section.

Through a combination of applying existing diagnostics (profile and
fluctuation) to non-tokamak magnetic configurations, further optimizing
existing diagnostics, and development of new diagnostics for as yet
unmeasured quantities, and direct comparison with turbulence
simulations, a more thorough understanding of the fundamental nature of
plasma turbulence will be obtained.

TABLE 1. Density fluctuation measurements on existing and developing
configurations

  --------------- ---------- ----------- ------------- ----------- -----------
                  Tokamak    Sph. Tok.   Stellarator   RFP         Spheromak

  Scattering      X          A           X             A           A

  Reflectometry   X          A/D         X             A/D         \-

  BES (beam)      X          D           A             \-          \-

  Probes          X          X           X             X           X

  PCI             X          A           A             A           A

  Thomson scat.   X          A           X             X           A

  CER (beam)      X          A           X             A           A

  ECE             X          \-          X             \-          \-
  --------------- ---------- ----------- ------------- ----------- -----------

X-Experimentally demonstrated, A-Applicable, D-Difficult, - Doesn't
apply

# Turbulence Control as a Means of Modifying the Plasma Pressure 

Every magnetic fusion concept could benefit from having some degree of
control of the plasma transport and the underlying turbulence. For some,
developing such capability is critical. For example, for the RFP,
confinement remains as one of the most pressing problems that must be
addressed if the concept is to achieve viability with respect to fusion
energy production. For tokamaks, dramatic improvements in confinement
have led to the realization that turbulence control has two other
important aspects beyond confinement improvement. First, advanced
confinement regimes are often characterized by pressure gradients that
are too steep, thereby lowering MHD stability margins. On the other
hand, steep pressure gradients are usually accompanied by large values
of the bootstrap current. A significant but often overlooked aspect of
this is that local transport changes in the core have proven to be the
most efficient means of driving current in toroidal devices. Significant
relaxation of the demands on external current drive systems might then
be achieved if the control tools for local turbulence manipulation and
transport control can be developed.

Several of the discussion points in the two Transport Working Groups
regarding the need for pressure profile control via turbulence
modification are expressed in the following excerpt from the summary of
the Workshop on Physics Requirements for Advanced Tokamaks, held at
General Atomics in March of 1999:

"The single issue that was virtually unanimously agreed to be the most
pressing in terms of the ultimate viability of the Advanced Tokamak is
the following: In both the experimental and modeling efforts, there
presently exists an inadequate understanding of the transport barrier
dynamics. (In particular), significant progress in advanced tokamak
research would result if local pressure profile control, through
manipulation of the local transport, can be realized. The requirement
for this control capability comes from the need to relax and broaden
local pressure gradients in order to realize the predicted gains in the
stability limits, while maintaining favorable bootstrap alignment with
the total current profile."

In addition, it was discussed at Snowmass that there is a need to
improve understanding of transport and transport barrier dynamics in
both core and edge plasmas of MFE devices. This effort implies
continuing and increased focus on dynamical modeling efforts of existing
experiments, as well as new investment in existing and novel fluctuation
diagnostics and the comparison of their measurements with codes that
calculate fluctuation spectral characteristics. Of primary concern,
though, is the development of the tools themselves that might be used to
modify the turbulence directly, thereby influencing the plasma pressure.

Required investments in control tool development -- The proposed
transport control tools that would most likely have success in a
reactor-scale device would be based on RF flow shear generation.
Experimental results that suggest that such a tool would be beneficial
can be found on the PBX-M tokamak, as well as recent results from FTU in
Italy. In both, launching of Ion Bernstein Waves is thought to be
responsible for generation of an ExB flow shear layer and an
accompanying reduction in transport. Direct measurements obtained on
TFTR with IBW indicate that such flow shear generation indeed can take
place. It was also noted that the TFTR experiments were hindered by
inefficient coupling of the directly launched wave to the core plasma.
This points to perhaps the most pressing problem related to IBW
research, namely, developing a means of efficiently coupling the IBW
antenna so there is efficient launch and deposition in the plasma core.

Other options for transport control, some of them more speculative and
some more appropriate for increasing transport when needed, include:
external coils for magnetic breaking or ripple, shallow pellet injection
to modify ELMs, impurity seeding which improves edge transport in some
cases, compact toroid injection or magnetically-insulated pellets to
modify core plasma parameters.

Significant clues that small amounts of externally provided flow shear
can have global consequences come from observations of self-generated
flows in existing or past experiments. Self-generated flow shears
observed in some H mode edges, such as DIII-D, and the TFTR and ASDEX-U
core plasmas suggest that significant global confinement changes can be
prompted by flow shear changes that begin on a spatial scale that is
significantly smaller that the device size. The global changes in
transport that result are a consequence of the plasma dynamics that
follow these localized changes. These observations provide some hope
that the favorable influence of ExB flow shear may not be intrinsically
more difficult to obtain in large, reactor-scale devices. Efforts to
modify the flow shear externally, with magnetic braking and with the
application of external torques via neutral beam heating demonstrate the
value of flow shear modification. In these experiments, flow shear
levels that were not as extreme as those that accompany the steepest
pressure gradients lead to moderated transport rates and thus pressure
gradients that did not challenge local stability margins.

Opportunities and needs- Despite the urgency expressed regarding the
needs for transport and transport barrier control tool development at
Snowmass, and the potential benefits if such a program succeeds, there
is little in place in the present MFE research program that suggests
this is a programmatic priority. It was noted that experiments are
planned on Alcator C-Mod using mode conversion IBW, but current RF
models are unclear on whether sufficient flow shear will be generated to
significantly modify transport in this case.

Research opportunities and needs appropriate for transport control tool
development and understanding include the following:

1\. A vigorous research program aimed at developing the antenna
technology for efficient, reliable coupling of IBW waves should be
pursued on at least one of the magnetic confinement device in the U.S.
community.

2\. The development of theory of RF wave physics needs to be supported
to further the understanding of IBW as a flow shear generation tool. In
parallel, such an effort should be directed at the identification of
other RF waves that might be suitable for such generation, while being
easier to launch. This theory development should occur in concert with
the experimental research program.

3\. A control tool research program should be accompanied by an
appropriate diagnostic set that enables the determination of the local
radial electric field and its shear, and perhaps the direct measurement
of RF-induced poloidal flows.

4\. Understanding of transport barrier dynamics will be significantly
enhanced if any means of modifying the flow shear in existing devices
can be found, even if they are not reactor-relevant. On DIII-D,
reorienting a neutral beamline so as to allow variable degrees of co-and
counter neutral beam injection would provide such flexibility.
Differences in transport barrier dynamics that will likely occur as a
result of changes in the core flow shear will serve as powerful tests of
transport dynamics models, increasing the confidence in projections to
more reactor-relevant scenarios.

# Interconcept Studies and Exploitation of New Devices

Although the various magnetic fusion concepts under investigation have
obvious differences, they also have much in common. Anomalous transport
occurs in most magnetic configurations, and in the rare attempts to
compare turbulent transport plasma behavior across different concepts,
similar features have appeared. For example, the electrostatic
turbulence in the edge of tokamak, stellarator, and RFP plasmas has very
similar characteristics, and in all three, this turbulence has been
shown to be the primary cause of particle transport, despite the
likelihood that the sources for this turbulence could be different. One
wonders if similar behavior occurs in other magnetic configurations, and
if universal physics models can be developed and applied, an example of
which might be self organized critical (SOC) transport models.

In support of the development of a predictive capability for turbulence
and transport in magnetically confined plasmas, the Summer Study
turbulence and transport groups identified interconcept studies as a
high leverage research element. The importance of such studies in
developing predictive capability is at least twofold. First, the
commonality ---and perhaps more importantly the differences---of the
various concepts provide diversity to develop and test robust, universal
models. For example, understanding the dominant electromagnetic
turbulence and transport in self-organizing plasmas such as the
spheromak and RFP might further the understanding of electron transport
in tokamak plasmas, for which the inclusion of electromagnetic effects
will be crucial. Second, physics understanding developed in more mature
concepts (both in terms of applied theoretical models and detailed
theory-experiment comparisons) will likely accelerate the understanding
of turbulence and transport in less mature concepts. For example,
understanding energetic particle modes (e.g., Alfven eigenmodes) at near
fusion conditions in tokamaks will develop models testable in the other
concepts. The success and/or failure of their predictions in other
configurations leads to refined model development. This strategy has an
important programmatic benefit. The present nature of fusion research
funding makes it much less likely (worldwide) that less mature concepts
will see the multiplicity of devices which formed the basis of empirical
scaling laws for transport in tokamak and stellarator plasmas. A
"smarter" approach based on first principles understanding may be the
only way to project performance for next stages of research, a logic
which equally well applies to tokamak and stellarator research.

With the commissioning of new devices comes the opportunity to further
leverage interconcept studies. The potential contributions of new
devices to advance predictive physics understanding should be identified
in the planning of both the research programs and facilities as a
proactive strategy. Such a strategy would help identify less obvious
opportunities, particularly those offered in alternate and emerging
concepts research. For example, a Summer Study presentation on Penning
trap confinement identified opportunities to study neoclassical
transport in new regimes of relevance to magnetic confinement. Truly
universal models can only be realized with a concerted effort to apply
and test them in many different configurations.

The need for plasma control tools and diagnostics to manipulate and
understand turbulence and transport is clearly important to virtually
every concept discussed. In a different sense of interconcept study
(maybe more appropriately termed cross communication), the development
and application of control tools and diagnostics could be made more
efficient and effective. As a particular example, plasma flow and/or
flow shear is a recurrent theme, either long recognized to be important
or anticipated to be important in almost every concept. Cross-concept
discussions of flow control and measurement would maximize opportunity
and minimize duplication. Other control measures (e.g., current profile)
are beginning to appear in the research plans for many of the concepts
and would benefit from fostered interconcept communication. A collateral
benefit of this approach would be deployment of diagnostics in a cost
effective manner, especially the most expensive diagnostics which might
not be required for every device in every concept. A nontrivial and
timely example is optical imaging diagnostics for fusion grade plasmas.
The competition between the need for large photon collection and
detector sensitivity and damage in a high radiation environment makes
such diagnostics challenging and expensive. Applied to smaller, hydrogen
plasmas they would be more economical. A well designed plan to implement
and compare results from such diagnostics across device and concept
lines would be highly valuable.

# I[ssues and]{.smallcaps} O[pportunities]{.smallcaps} S[pecific to]{.smallcaps} MFE C[oncepts]{.smallcaps}

The following sections outline issues and opportunities that were
identified during a systematic review of each magnetic confinement
configuration. These have necessarily de-emphasized the over arching
issues that were covered in detail above. What remains, are issues that
are of particular importance to particular configurations. The level of
detail and the relationship of theory and experiment vary from section
to section as is appropriate for the level of development of each
concept.

# Tokamak

Tokamak research has led to and benefited from significant progress in
the understanding and control of transport. With the extensive
diagnostic set in current tokamaks, detailed measurements contribute to
the understanding of transport phenomena including the relationship
between turbulence and transport, and mechanisms affecting transport in
different channels. In several "advanced" regimes obtained in tokamaks,
transport (ion thermal, particle, angular momentum) has been reduced at
the edge (H-mode, VH-mode, etc.), in the core (PEP, ERS, NCS, high β~P~,
etc.) and throughout the entire plasma (NCS and high β~P~ H--modes).

Future progress on the tokamak will address both cross-cutting transport
issues and further application of our understanding toward improved
fusion performance. In doing so, we will address several remaining major
challenges:

Understanding of tokamak transport and the development of an improved
predictive capability.

Considerable effort has gone into testing physics-based models against
observations made in tokamak experiments. So far, no model has been
successful in describing the full set of observed behaviors. In
particular, physics-based simulations of electron thermal and particle
(electron, main ion and impurity) transport have not been developed and
tested as extensively as those of ion thermal transport. Addressing
these and other issues will require increased emphasis on physics either
not currently included or insufficiently treated, such as
short-wavelength turbulence (eg. electron temperature gradient, or ETG
modes), electromagnetic dynamics and more realistic geometry. More
detailed simulations will also require the plasma community to take
advantage of advances in computer technology.

At the same time, experiments must be better prepared to test
theoretical predictions. Observations of fluctuations in the generic
spatial and frequency range expected for drift/ITG instabilities have
been observed, but direct observations distinguishing the ITG (ion
temperature gradient) mode from other modes have not been made Direct
observations are also lacking for ETG modes, and for the zonal flows
which are predicted to damp long wavelength modes. Such tests of
theoretical predictions may, in some cases, require the development of
new diagnostics. Diagnostic areas identified for improvement include the
ability to observe small-scale turbulence, and increased capability to
image turbulence in two dimensions. Most of the current diagnostics,
especially in the core, are sensitive only to density fluctuations. A
more complete picture requires measurements of other fluctuating
quantities, including temperature (ion and electron), electric potential
and magnetic field.

In the past, extrapolations of plasma behavior to new (larger) devices
were done largely through the use of empirical scaling relations. A more
reliable predictive capability based on scientific understanding is
needed. An intermediate strategy has also been identified. By choosing a
set of dimensionless parameters to describe the plasma, it is possible
to construct an experiment that matches most of the dimensionless
parameters expected in a next-step or reactor class device. Typically,
the one such parameter that cannot be matched with a reactor is ρ\*, the
normalized ion gyroradius. "Dimensionless scaling" experiments have been
done in several devices to empirically determine the scaling of
transport with just this one parameter. "Dimensionally identical"
discharges have also been produced in several devices, generally
supporting the usefulness of these scalings. However, some papers on
modeling of such dimensionless scaling experiments have shown that
moderate changes in other dimensionless parameters (such as the
rotational Mach number, density profile shapes, or Ti/Te) can introduce
uncertainties into these extrapolations. Further progress in this
approach requires more precise profile measurements on multiple devices,
particularly in the edge/pedestal region.

Basic transport processes

Transport in tokamaks is characterized by an irreducible minimum level
set by neoclassical theory, which is overlaid by "anomalous" transport
processes believed to be primarily turbulent in nature. Until recently,
the anomalous component of transport dominated, so that neoclassical
predictions of transport were considered irrelevant.

Much progress has been made in understanding ion thermal transport
during the last decade. Many observations are consistent with the
hypothesis that the "anomalous" ion thermal transport is driven largely
by ITG modes, which can be suppressed by sheared **E**×**B** flows.
Fluctuation measurements are roughly consistent with the ITG hypothesis,
but conclusive proof of the hypothesis is still lacking. With advances
in transport suppression (see "Transport barriers," below), turbulent
transport has been eliminated in many cases, at least for the ions. This
leads to a situation in which neoclassical transport can once again
become important. It also exposes areas where neoclassical theory is
weak and needs improvement. One well-known example is the need for
inclusion of "orbit squeezing" effects near the axis in discharges with
reversed magnetic shear.

Our understanding of behavior in the electron channel is less advanced.
In many regimes, it is thought to be due to the non-adiabatic electron
response to ITG turbulence due to trapped-electrons or finite-beta
effects on passing electrons, though more work is needed to do
quantitative tests of this. But there are many cases where ITG
turbulence is stabilized by sheared flows, and ion thermal and electron
particle transport is significantly reduced but the electron thermal
transport is still anomalous. Although ETG turbulence, analogous to the
ITG mode, is a hypothesized candidate to drive electron thermal
transport in some cases like this, this is less certain. One difficulty
is that ETG modes are predicted to appear at very short wavelengths,
beyond the range of most current fluctuation diagnostics. Another issue
is that other phenomena, both electrostatic and electromagnetic, are
also predicted to impact electron thermal transport but are similarly
difficult to observe.

Recent theoretical work has proposed several mechanisms that may control
transport in tokamaks and other devices. One such phenomenon is
self-organized criticality, in which discrete avalanche-like events can
determine the plasma profiles. This may be supported by observations of
self-similar turbulent spectra in plasmas, with similarities between
different experiments and regimes. Zonal flows have been proposed as a
possible mechanism for the transport to become self-limiting. In this
case, the turbulence itself can generate localized flows, which then
feedback on the turbulence through sheared **E**×**B**. Unfortunately,
the ability to test this prediction remains a challenge for future
diagnostics.

Transport barriers

Achievement of transport barriers, in many cases with ion thermal
transport reduced to neoclassical levels, is a recent triumph of
transport physics. The hypothesis that **E**×**B** shear stabilizes the
long-wavelength turbulence responsible for ion thermal transport
qualitatively explains the formation of these regions, and can describe
much of the observed dynamics. Simple models have been created which are
beginning to predict such bifurcations, but a complete, time-dependent,
self-consistent model of transport barrier formation still does not
exist.

Understanding of these regimes is complicated by the complex interplay
between different terms of the **E**×**B** shearing rate and other
factors affecting the microinstability growth rates, resulting in a set
of multiple feedback loops. Edge transport barriers (H--mode) are even
more difficult to describe, due to the additional complexity associated
with high neutral populations and divertor geometry which require a 2--
or even 3--D description.

Applicability of core transport barrier regimes in future reactor
scenarios depends on our ability to control the barrier position and
characteristics. In some cases, we may need the capability to *increase*
transport in the barrier region in order to avoid MHD instabilities
associated with strong pressure gradients. Also, control of the barrier
position will be important both for maximization of fusion performance
and for MHD stability considerations.

Tools for transport barrier control will need to be developed. An
important consideration here will be compatibility of pressure and
current profile control tools, since both will be important in obtaining
a sustained high performance regime. Compatibility with "next-step" and
reactor class devices is another important consideration.

Fusion reactors, as currently envisioned, will operate with electron
temperatures slightly higher than the ion temperature. In contrast, most
core transport barriers thus far have been associated with "hot-ion"
regimes (*T*~i~ / *T*~e~ \>\> 1). This is perhaps to be expected, due to
enhanced stability to the ion temperature gradient (ITG) mode expected
in such conditions. Nevertheless, in a small number of cases, core
barriers have been created with near equal electron and ion
temperatures. Although such regimes are more speculative,
reactor-relevant hot ion regimes may be possible and could have a high
payoff. Such regimes may depend on undeveloped technologies such as
"alpha channeling," or might just rely on poor transport in the
electrons and nonzero alpha heating of ions (and require higher alpha
power to make up the losses).

Another issue that has been raised is that of flow generation in a
reactor-sized device. This may also require the development of new
technologies, such as RF-driven flows. The problem may be lessened by
improving the efficiency of the tokamak ("Advanced Tokamak") in order to
allow a smaller device size.

Density limits

Density limits observed in many tokamaks are not yet fully understood,
but there is some belief that the underlying physics is at least
partially a transport effect, in the sense that both turbulence and
transport typically are seen to scale as *n*/*n*~C~, as the density *n*
approaches a critical value *n*~c~. It may represent a more basic issue
than the plasma current limit for a specific MHD equilibrium. Since this
effect imposes an operational boundary that is directly related to
fusion yield, progress in this area represents a high-leverage
opportunity for future reactor performance improvement. As experiments
move more towards high performance, long-pulse to steady-state
discharges, more theoretical and experimental work are needed to
elucidate this issue.

Today's large tokamaks are outfitted with advanced, high power heating
systems and extensive diagnostic sets. This allows study of plasma
behavior under conditions most similar to those in a reactor. Continued
study of these issues will allow not only further performance
improvements to the tokamak, but should also provide an improved
physical understanding of transport processes in fusion relevant plasmas
which will be applicable to other confinement concepts.

# Spherical Torus/Tokamak (ST) 

The Spherical Torus has unique transport properties associated with very
low aspect ratio, high equilibrium sheared flows, and high beta. Its
parameter domain is characterized, under the best of circumstances, by
order-unity local plasma β, absolute \"magnetic well\" up to 40%, and
dielectric constant up to \~10^2^. Theoretical studies predict flow
shearing rates up to and above 10^6^/s, fully aligned ∇p-driven current
profiles up to 100% of the plasma current, and supra-Alfvén energetic
and possibly thermal particles. The investigation of the Spherical Torus
plasmas therefore promises opportunities to advance plasma transport
studies.

The Snowmass Summer School discussions by the MFE transport sub-topical
group identified transport issues and opportunities for the Spherical
Torus. The issues and opportunities were categorized as (1) Edge
transport barriers, (2) Suppression, and possible stabilization of
micro-turbulence, (3) Hydrodynamic turbulence from large flow and
energetic particles, (4) Core transport barriers, (5) Theoretical and
computational needs, and (6)Diagnostic and transport measurements. Some
of the issues and opportunities are not unique to the ST. There wasn't
any discussion prioritizing the issues and opportunities.

1 Edge transport barriers

Several issues related to the ST's particular characteristic of low
magnetic field and aspect ratio were identified which will be important
in understanding edge transport barriers and H-mode in the ST. The low
magnetic field gives rise to a large normalized ion gyroradius compared
to the Tokamak Since there are theoretical and experimental scalings of
H-mode threshold and edge parameters dependent upon the ion gyroradius,
the ST provides a useful extrapolation of these quantities. Furthermore,
experimental study of the edge parameters and power threshold for the
H-mode in present ST experiments will facilitate the design of future ST
devices. However, the potential for naturally occurring large plasma
flows, flow shears, and magnetic shear may naturally suppress transport
and may make the H-mode less valuable in the ST.

\(2\) Suppression and possible stabilization of micro-turbulence

There are a number of mechanisms that could suppress and possibly
stabilize micro-turbulence even though the small aspect ratio results in
a higher trapped particle fraction which can drive higher levels of
transport. The diamagnetic flows in the ST could reach sonic values,
leading to the possibility of relatively larger shearing rates to
suppress microturbulence. Furthermore, the inherent orbit-averaged good
curvature at low aspect ratio could stabilize micro-instabilities as
well. Considering the high trapped particle fraction and multiple
microturbulence suppression mechanisms it will important to characterize
the turbulence in both the edge and core of ST plasmas.

3 Hydrodynamic turbulence from large flow and energetic particles

The low magnetic field in the ST will lead to relatively smaller
Alfvenic flows which could destabilize hydrodynamic turbulence and lead
to energetic particle driven instabilities (e.g. TAE). The confinement
of energetic particles in the present of this class of instabilities
could be a major issue for the ST.

4 Core transport barriers (both ion and electron)

The much enhanced flow shearing rates in the ST plasma are expected to
suppress the micro-turbulence and possibly return the heat and particle
transport toward the level of the neoclassical model. These conditions
are critical for the formation of core transport barriers in recent
Tokamak experiments. However, in those experiments the relative
importance of magnetic shear and ExB shear is not clear. ST experiments
will be able to explore this issue rather thoroughly, since they have
inherently wide ranges of ExB and magnetic shears available in
MHD-stable equilibria. Furthermore, in proof-of-principle ST experiments
neoclassical transport may likely be a major contributor to the total
radial transport regardless to the status of the collisional transport.
Consequently, transport barrier formation may be problematic in these
experiments and may only emerge in Performance Extension experiments.
Therefore, in the proof-of principle experiments it will necessary to
characterize the turbulence in regimes with high flow shear.

5 Theoretical and computational needs

ST plasmas have local beta \~ 1 and plasma flows with speeds comparable
to the Alfven (and thermal) velocities. Such plasmas are ubiquitous in
nature (e.g., in astrophysical and magnetospheric contexts), and have
been studied extensively in other communities. Typically, particular
emphasis has been placed on hydrodynamic calculations. It is exciting to
realize that the development of turbulence and micro-instability theory
and computation for the ST will likely be influenced by and contribute
to these related fields. There are many opportunities for synergistic
developments, particularly with respect to developing turbulence and
transport simulations that are directly relevant to astrophysical and
magnetospherical systems, and that can be tested in the laboratory.

6 Diagnostic and transport measurements

Experiments focusing on the transport issues in the ST need to be
integrated into experimental plans. This includes both heat and particle
transport studies using both steady-state and perturbative analysis
techniques. The ST's unique characteristics may necessitate alteration
of the diagnostics currently in use in the Tokamak. The low magnetic
field in the ST has motivated research into new diagnostic techniques to
measure the current profile and the electron cyclotron emission.

# Stellarator

With the construction of two \$1B class stellarators, LHD and W7-X,
stellarators are playing an increasingly significant role in the world
fusion program. Stellarators present unique challenges and opportunities
in the area of transport and turbulence.

From the transport perspective, the primary difference between
stellarators and axisymmetric configurations is their relatively large
neoclassical transport losses, due to ripple trapped particles in the
non-axisymmetric local magnetic wells. This leads to an unfavorable
(1/**ν**) temperature scaling of neoclassical transport which becomes
large in the core of current experiments. Recent stellarator experiments
have shown that measured transport is consistent with neoclassical
levels in the core, but transport remains anomalous in the edge, where
it is due to turbulent fluctuations.

Future experiments are designed to significantly reduce neoclassical
losses by optimizing the magnetic geometry and exploiting symmetries:
quasi-axisymmetry (QAS), quasi-helical symmetry (QHS), and
quasi-omnigeneity (QOS) are among the approaches currently being
considered. A major goal of the stellarator program is to verify to what
extent these symmetries can reduce neoclassical transport, both to test
the neoclassical theories, and to test whether the required degree of
symmetry can be achieved in an actual experimental realization. For
eventual reactor considerations, a cross-cutting issue is achieving good
transport at high beta, consistent with MHD stability calculations.

Another clear goal is to compare turbulence simulations and theory with
transport and fluctuation measurements on stellarators. Since the
neoclassical transport in future stellarators is predicted to be
reduced, turbulent transport is expected to play a larger role in future
devices, strengthening the links between transport studies in
stellarators and tokamaks. Relative to similar experiments in tokamaks,
quantitative comparisons of this sort on stellarators are in their
infancy. There is a strong need to develop theoretical and numerical
tools (3D turbulence simulations and transport analysis codes) and
fluctuation diagnostics. Stellarator geometry is more complicated, but
since many codes now treat general geometry numerically, this is to some
extent a detail, and not a fundamental development issue. More work is
clearly needed in this area.

The stellarator has unique issues associated with transport barrier
control and formation. In tokamaks, there is an interaction or feedback
loop involving transport, pressure gradients, bootstrap currents,
current profile evolution, and MHD stability which can be difficult to
control, but has lead to the formation of transport barriers, turbulence
suppression, and enhanced performance. The stellarator breaks this loop
to some extent, since the q-profile (and magnetic shear) is controlled
mostly externally, and therefore the problem of q-profile evolution and
MHD stability is likely to be less challenging compared to tokamaks. It
is not clear, however, that stellarator experiments can be designed with
sufficient magnetic flexibility to achieve a comparable degree of
q-profile variation transiently available in tokamak experiments.

A perhaps more significant difference is in the physics determining the
radial electric field in stellarators. Since ExB shear suppression of
turbulence is the primary candidate for transport barrier formation,
this may change the conditions required to produce barriers. Tokamak
neoclassical transport is intrinsically ambipolar, and the plasma is
free to rotate toroidally so that the radial electric field is in
equilibrium with the flows and the pressure gradient. Standard
stellarator neoclassical transport is not intrinsically ambipolar, and
the radial electric field adjusts until the transport becomes ambipolar,
i.e., the plasma charges up until E_r enforces ambipolarity. The E_r
which achieves this balance is not unique, and there are usually two
stable roots: the \"ion root\" where E_r holds in the ions and ion
energy confinement is good, and the \"electron root\" where E_r holds in
the electrons and electron energy confinement is good. For standard
stellarators, a key issue is to demonstrate whether or not the ion root
is consistent with transport barrier formation and turbulence
suppression. For Q{AHO}S, the key issue is the following: what degree of
symmetry is required to restore (quasi-) intrinsic ambipolarity and
freedom of rotation (not toroidal, but in some twisted direction)? If
this is achievable, transport barrier formation in stellarators could be
very similar to tokamaks.

# 

# Electric Tokamak (ET)

The goal of the Electric Tokamak (ET) is to induce a bifurcation \[1\]
into a *global* enhanced confinement regime by forcing a strong radial
electric field via non-ambipolar ICRF-induced fast ion orbit loss.
Because the poloidal flow damping in tokamaks is dominated by trapped
particle magnetic pumping, if the bulk plasma rotates faster than the
trapped particle bounce frequency, then the poloidal flow damping is
greatly reduced because of the destruction of trapped orbits. The plasma
will remain in this state even when the drive is greatly reduced. In
addition, Ion Temperature Gradient (ITG) modes will be eliminated at
high poloidal rotations if the drive provided by resonant trapped ions
is eliminated \[2\]. Shear in both toroidal and poloidal rotation will
also be present and beneficial for reducing ion turbulence. This method
of inducing a bifurcation by forcing poloidal rotation over the maximum
in the damping has been done successfully on CCT \[3\] and other
machines: only edge bifurcations induced in those past experiments. The
ET experiment is designed with a high aspect ratio (\> 5) in order to
have a low magnetic pumping and is optimized for a *global* bifurcation
\[2\]. Partly because the fast particle banana width is the same size as
the minor radius, it should be easier in ET to produce the required ion
orbit loss than in other tokamaks. The major issue for this experiment
is therefore whether this scheme (successfully applied with edge probe
biasing) can be extended into the core plasma with ICRF heating.

The resulting strong flow profile can then be controlled through
adjustments in the neutral particle density and fully adjustable ripple
for toroidal motions. Spectroscopy, reflectometry, and probes will be
used to measure these fluctuations and flows with likely upgrades to
other techniques as warranted. Because of the high aspect ratio and
large volume (\~ 180 m^3^), there will be up to 64 m^2^ of antenna space
both *inboard* and outboard for better coupling. Direct momentum input,
and current drive as well as ion orbit loss and heating will be
explored. The inboard RF launch can also be used for marfe control and
therefore density limit control. This unique inboard access can also be
employed for a full 2-D picture of the fluctuations.

Once in a fully bifurcated state, the beta should increase. Given that
stability requirements are satisfied \[4\], the beta should rise to near
unity where it becomes omnigenous (ions drifts are locked to the
magnetic surfaces: therefore classical confinement). The elimination of
ion trapped orbits likewise eliminates both ion anomalous as well as ion
neoclassical transport. With the large effective aspect ratio due to a
high beta magnetic well, electron anomalous transport is reduced but
likely not eliminated. The ET experiment is an exploratory experiment
and will therefore need to face issues related to the above-described
scheme ahead of theory development. In response, theory development
should be catalyzed by ET results.

\[1\] K.C. Shaing and E.C. Crume Jr., Phys. Rev. Lett. 63 (1989) 2369.

\[2\] M.W. Kissick, et al., submitted to Phys. Plasmas.

\[3\] R.J. Taylor, et al., Phys. Rev Lett. 63 (1989) 2365.

\[4\] S.C. Cowley, Phys. Fluids B 3 (1991) 3357.

# Reversed Field Pinch (RFP)

Core transport (r/a \< 0.8): RFP\'s and other q \<1 configurations
typically exhibit large-amplitude magnetic fluctuations. In the RFP,
these fluctuations are believed to be responsible for sustaining the
reversed-toroidal-field configuration through (dynamo) current drive.
However, these same fluctuations drive most or all of the core particle
and energy transport, which is typically about 100 times larger than the
classical prediction. The dominant magnetic fluctuations are
core-resonant, global tearing modes with poloidal mode number m = 1 and
toroidal mode numbers n \~ 2R/a. These modes are believed to be driven
by a gradient in the parallel current profile. When these modes grow to
sufficient amplitude, their associated islands overlap, stochasticizing
the core. We have little information on electrostatic fluctuations in
the core, but in standard-confinement discharges, they are believed to
contribute little to transport. In improved-confinement discharges,
however, core magnetic fluctuations decrease, so the electrostatic
fluctuations may begin to play a greater role. At present, the reduction
of core particle and energy transport is focused on reduction of
magnetic fluctuations.

Edge transport (r/a \> 0.8): Particle transport in the RFP plasma edge
is governed by electrostatic fluctuations, as in other configurations,
but the origin of these fluctuations in the RFP is not yet known. The
cause of energy transport in the edge has not yet been identified, as
measurements so far indicate that neither magnetic nor electrostatic
fluctuations contribute. However, the electrostatic measurements for
energy transport only extend into r/a \~ 0.9. In the region r/a \> 0.9,
energy transport may be governed, e.g., by parallel losses due to
magnetic field errors. In the region r/a \< 0.9, electrostatic
fluctuations may yet be important. Several challenges remain with
respect to the plasma edge: (1) identifying the origin of electrostatic
fluctuations, (2) reducing particle transport through control of
electrostatic fluctuations, and (3) identifying the source of and
reducing edge energy transport.

Reduction of core and edge fluctuations: Confinement in the RFP has been
improved at least five-fold with the addition of auxiliary parallel
current in the plasma edge. This auxiliary current is driven with a
technique called pulsed poloidal current drive (PPCD), the goal of which
is to flatten the edge current profile to reduce the core-resonant
tearing fluctuations. Although it provides only coarse control of the
current profile, PPCD is quite successful in reducing these
fluctuations. With the goal of further reducing the core fluctuations
beyond what is possible with PPCD, radio frequency current drive
techniques are under development which could allow finer tailoring of
the current profile. Sustainment of the RFP magnetic configuration
requires some form of edge current drive, and this is normally provided
by the tearing modes. One can view PPCD, or any externally driven edge
current, as a replacement for the tearing mode current drive, which
thereby obviates the need for the tearing fluctuations. In addition to
PPCD discharges, there are also discharges with improved confinement
that occurs spontaneously, without auxiliary current drive. These
discharges also exhibit reduced core tearing fluctuations. In addition,
there is a region of strongly sheared E x B flow in the plasma edge and
an edge-wide reduction of electrostatic fluctuations. It is now known
that PPCD discharges also possess a similar region of flow shear and
reduced edge electrostatic fluctuations. There are many questions that
must be answered in order to understand the confinement improvement in
these discharges. For example: (1) in improving energy confinement, what
is the contribution of reduced core fluctuations relative to reductions
in the edge? (2) can flow shear contribute to improved energy
confinement in the RFP, as it does in other configurations?

Transport modeling: To better understand the issues described above, we
need improved modeling of local transport. This will require much more
detailed measurements of equilibrium profiles and fluctuations, and
diagnostic upgrades are underway to address this need. Using these
measurements and a 1D transport code, we will be able to calculate local
transport and compare with local measurements of fluctuations.

Computational/theoretical issues: There is a plethora of outstanding
computational and theoretical issues related to transport in the RFP,
many of which are directly related to the issues described above. One
challenge is to improve the ability of MHD modeling codes to simulate
plasmas with experimentally relevant parameters, for while existing
codes reproduce several basic features of RFP discharges, like toroidal
field reversal, there are some important features that the codes do not
predict. One code-experiment parameter difference that stands out is the
Lundquist number (S, the normalized conductivity). Because of practical
limits on computational speed, the codes are limited to S \~ 10^4^,
while S reaches \~ 10^7^ experimentally. Beyond simply matching the code
and experimental parameters, simulation of higher-S plasmas is important
to test the idea that the core tearing fluctuation amplitudes could
scale inversely with S, which would be favorable for an RFP reactor.
Assuming that this computational problem is soluble, these codes can be
applied to the task of finding an optimal RFP configuration, in terms of
the current, pressure, and flow profiles and in terms of the plasma
shape and aspect ratio. Optimally, these simulations will be carried out
with a code that incorporates two fluids, and such a code is presently
under development. Also of potential relevance to the RFP and other
configurations is the extension of gyrofluid and/or gyrokinetic codes to
model electromagnetic turbulence. Theory can also help to identify the
cause(s) of electrostatic fluctuations in the plasma edge, studying the
possible influence of, e.g., localized interchange turbulence.
Theoretical work is ongoing to describe the mechanism by which flow
shear occurs spontaneously in the plasma edge, as well as the possible
effect of this flow shear on both electrostatic and magnetic
fluctuations at large and small spatial scales.

# Spheromak

The spheromak is a toroidal configuration in which plasma current is
driven by a dynamo associated with the inward transport of helicity from
the edge plasma. Associated with this transport are magnetic
fluctuations which break the axisymmetry of the plasma and, by opening
magnetic surfaces allows the outward transport of energy. The
reconnection events associated with these fluctuations cause anomalous
ion heating. (If controlled, this heating might be utilized in hot
spheromaks.) An analysis of the decaying plasma in the final CTX devices
found that the cross field losses were consistent with
Rechester-Rosenbluth diffusion of electron energy in the presence of
magnetic field fluctuations which scaled with the Lundquist number, *S*,
as
$\left| \overset{\sim}{B}/B \right|\text{\textasciitilde}S^{\pm \alpha}$,
where ![](media/image1.wmf). This scaling would lead to an interesting
reactor; however, the database is very limited so that the loss
mechanisms have not been unambiguously identified, and the scaling is
highly uncertain. Further, measurements in a sustained plasma are
insufficient to even estimate the scaling in a regime interesting to
fusion. There are no measurements of electrostatic fluctuations in a
spheromak.

The spheromak can be sustained by injection of helicity from a coaxial
"gun," in which a source of helicity is applied across a gap in the flux
conserver in the form of a voltage-poloidal flux product. This helicity
is carried into the spheromak separatrix by a kink-like, *m* = 1
instability of the current column driven by the injector. Some
measurements suggest that the helicity is then transported throughout
the toroidal volume by short-scalelength fluctuations, generating the
dynamo and balancing the resistive plasma losses.

In the limit of localized (short-scale) magnetic fluctuations (and low
beta), the inward helicity transport is predicted to be proportional to
∂(*j*~\|\|~/*B*)/∂ψ, where *j*~\|\|~ is the current density along the
magnetic field, **B**, and ψ is the flux. This gradient is also the
driving term for tearing (reconnection) modes which are believed to be
the primary source of the fluctuations. In the sustained spheromak, the
*q*-profile need not have an internal, resonant *m* = 1 surface. In that
event, the fluctuations should be relatively short-scale and it would be
valid to describe the inward helicity and outward energy transports as
diffusive. Thus, although spheromak physics is closely related to that
in the RFP, if this holds the differences in detailed operation may
yield significant differences in energy transport.

The highest electron temperatures (\~ 400 eV) were obtained in CTX on
after reduction of magnetic field errors by careful flux conserver
design and control of impurities and of edge neutral density by wall
conditioning and gettering. Further evidence that the fluctuations were
relatively low was that ion and electron temperatures were comparable,
whereas in earlier experiments the ion temperature was \>\> than the
electron temperature. Unfortunately, the CTX experiment did not continue
after obtaining these results. A new experiment, SSPX, has been started
to determine the detailed mechanisms and their scalings with *S* and
other plasma parameters. An extensive set of profile diagnostics are
being assembled to measure the density, temperature, and magnetic field.
Measurements of magnetic fluctuations, both by wall-mounted magnetic
probes and in the volume by x-mode reflectometry and a Transient
Internal Probe will provide data to relate the profile-determined
transport coefficients to the fluctuations. Results from this experiment
will also contribute to basic plasma science of interest both to fusion
and to astronomical plasma physics.

The experimental measurements of transport and its close association
with magnetic fluctuations need to be supported by calculations of 3D
resistive MHD, e.g. as being carried out by the NIMROD code (and
discussed in the MHD Snowmass groups). Such codes, properly benchmarked
with experiment, will provide a basis for understanding transport
scaling with plasma parameters and modes of operation. The effects on
transport and energy losses of plasma flows and non-ideal processes will
need to be explored.

# Field Reversed Configurations (FRC)

*Two-fluid relaxation*

The FRC may be describable as a minimum energy state in a two-fluid
context. A key element of the two-fluid theory is the existence of a
magnetofluid invariant for the ions (ion self helicity), combining
magnetic and mechanical (flow) parts, in addition to the usual magnetic
helicity. *Issues*. 1) Measurements of the ion self helicity (magnetic,
flow profiles) are needed. 2) What is the nature (spectrum, distribution
of mode type) of the relaxation turbulence? 3) Measurements of the
turbulent fluctuations are needed. 4) What is the transport from the
turbulence? 5) Will the FRC minimum energy state evolve toward a Taylor
state (*e.g*. a spheromak).

*Spontaneous flow-shear generation*

A predicted feature of the two-fluid relaxation is global flow and flow
shear. This may appear spontaneously in FRCs. *Issues*. 1) Is sheared
flow spontaneously generated in FRC experiments, and does it arise in
some magnetic configurations and not in others? 2) Will this flow have a
stabilizing effect on turbulence? 3) Measurements to detect the flow and
flow shear are needed.

*Theoretical needs*

The value of the two-fluid relaxation theory hinges on the ruggedness of
the ion self helicity. *Issues*. 1) The ruggedness of the self helicity
needs to be tested in two-fluid codes. 2) Is there a statistical
description of the relaxation turbulence? 3) Are relevant theoretical
results available in other contexts resembling the FRC, *e.g*. space
plasmas?

*Role of scrape-off-layer (SOL)*

The FRC is embedded in a magnetic mirror with open field lines forming a
SOL. It is likely that rapid outflows in the SOL plasma will prevent it
from conforming to a state of minimum energy. *Issues*. 1) Do gradients
in the SOL cause turbulence which governs global transport by regulating
a continuous low-level of relaxation in the core plasma? 2) Does the
relaxation proceed continuously or by intermittent events, and what are
the transport implications? 3) Can this edge turbulence be controlled if
need be?

*Classical transport*

The ion gyro-radius is relatively large in FRCs: *ρ~i~/a \> 1/5* in
present experiments and \> 1/40 is expected for reactor. *Issue*. Is the
classical transport (the irreducible minimum) significant?

*Diagnostics and transport measurements*

*Issue*. What types of diagnostics will be effective to measure and
characterize the transport in FRCs?

# Levitated dipole

The levitated dipole has been predicted to have excellent (possibly
classical) confinement which would make it an candidate for burning
advanced fuels (like Dhe^3^). Since the confining magnetic field is the
field of a floating ring, there is no toroidal field and therefore there
are nor drifts off of flux surfaces which leads to the \"neo-classical\"
degradation of confinement present in tokamak-like systems.

A unique feature of a dipole is that MHD stability results from plasma
compressibility. As a result the pressure gradient between the pressure
peak and the vacuum chamber wall has to be relatively gentle in order to
maintain MHD (interchange) stability and it is expected that the device
will operate near this critical pressure gradient. The MHD stability
requirement can be shown to require that ω\* \< 2 ω~K~ with ω\* the
diamagnetic drift frequency and ω~K~ the curvature drift frequency.
Recent theoretical analyses \[Kesner, Phys Plas 4, (1997) 419; 5 (1998)
3675\] have indicated that this criterion also predicts the stability of
the low beta drift modes. Therefore one can conjecture that when a
dipole plasma is MHD stable it is also devoid of drift wave driven
transport.

An interesting complication of confinement in a levitated dipole system
is the possibility of convective cell formation, as has been observed in
systems that have closed field lines \[see for example G. Navratil, R.S.
Post and A. Butcher Ehrhardt, Phys Fluids, 20 (1977) 157.\]. In this
regard it is important to observe that convective cells primarily
transport particles. In fact in the marginally MHD stable equilibrium
convective cells would only transport particles (no energy transport).
In a reactor, for example, convective flows could would move ash outward
(while cooling) and move fuel inward (while heating) toward the fusing
region of hot plasma.

**Scheduled speakers and discussion** **leaders**

Discussion leaders for the morning MFE Transport Subgroup were:

> Tokamaks - Chuck Greenfield,
>
> ST - Phil Efthimion
>
> Stellarators - Alan Boozer
>
> ET - Michael Kissick
>
> RFP - Brett Chapman
>
> FRC - Loren Steinhauer
>
> Spheromak - Bick Hooper
>
> Dipoles - Jay Kesner

Discussion leaders and discussion recorders for the afternoon Transport
and Turbulence Science Subgroup included Glenn Bateman, Mike Beer, John
DeGroot, Darin Ernst, Greg Hammett, Jim Lyon, David Newman, Scott
Robertson, Gary Staebler, Ed Synakowski, Paul Terry, Richard Town. The
overview speakers for the afternoon Transport and Turbulence Science
Subgroup were:

MFE overview Jim Drake: Turbulence and Transport: a theory/computational
perspective

MFE overview Ed Synakowski: Transport physics needs and goals in
magnetic fusion energy research over the next 5-10 years

IFE overview Bill Kruer: Waves-Particle Interaction and Turbulence
Issues and Opportunities in Inertial Fusion

IFE overview Jean-Pierre Matte: Transport Issues in ICF Plasmas:
Overview of past work and of unsolved problems.

IFE overview Sigfried Glenzer: Transport Experiments in ICF

Shorter contributed presentations:

Glenn Bateman: Issues for Predictive Transport Modeling

Juan Fernandez: Wave and Turbulence Experiments in ICF Plasmas: Research
on saturation mechanisms for stimulated Raman scattering

Paul Terry: Issues in turbulence and transport with wider scientific
implications

Bill Tang: Opportunities in turbulence simulations

Max Tabak: Fast Ignitor Theory

Mike Key: Fast Ignition Energy Transport Experiments

Jim Hammer: Transport in hohlraums/effects of magnetic fields

George Morales: Plans and rationale for a basic science facility

Stewart Zweben: Search for new plasma turbulence diagnostics

Amiya Sen: Need for better nonlinear dynamic models of plasma
turbulence, and some promising experimental methods towards it

Stan Luckhardt: 2D and 3D imaging of plasma modes and turbulence: grand
diagnostic challenge 2000-2010

Leonid Zhakharov: Liquid wall effects on transport and plasma behavior

David Newman: Improved methods for theory/simulation/experiment
comparisons.

Greg Hammett: Opportunities for comprehensive simulations and
experimental tests

Scott Parker: Synergies in Kinetic-MHD and Turbulence Simulation

Jim Callen: Future of Plasma Simulations = Chapman-Enskog-like approach?

Wally Manheimer: A Distant Mirror, Some Medieval Thoughts on Marginal
Stability and Macro/Micro Interactions

Ron Cohen: Joint discussion with plasma boundary group on boundary
turbulence, etc.

# Acknowledgement

The authors would like to acknowledge the contributions of all the
transport breakout group members who participated in the discussions
summarized here.

## 

[^1]: ^^ This is the list of authors who participated more directly in
    writing assignments for this summary report. This summary is based
    on the presentations and discussions in two working groups at
    Snowmass involving a larger group of people. Most of the scheduled
    speakers and discussion leaders are listed at the end.

[^2]: ^^ The term "predictive transport modeling" in MFE has generally
    been used to refer to transport codes that use models of transport
    coefficients (along with calculations of sources and sinks such as
    auxiliary heating and atomic physics) that can be used to "predict"
    the temperature and density profiles in past or future experiments.
    This term has been used to distinguish it from "interpretive
    transport modeling", where the measured temperature and density
    profiles are combined with detailed calculations and measurements of
    the sources and sinks in order to determine what the transport
    coefficients must have been in a given experiment. "Predictive
    transport modeling" is also used somewhat to distinguish it from
    purely empirical transport scalings, particularly 0-D global
    scalings. But because many existing predictive transport models are
    often semi-empirical (with a theory-motivated scaling but
    supplemented by adjustable coefficients that are empirically fit to
    past experiments) or are not yet complete enough to calculate the
    full profiles (and so are supplemented by measurements or empirical
    scaling for edge boundary conditions, etc.), there is a sense in
    which they are not fully predicting new phenomena, though even an
    empirical scaling makes a "prediction" when extrapolated to a new
    experimental regime or to an experiment which has not yet been
    built. It is difficult to know the limits of validity of empirical
    models, and the complete physics is so complicated that a single
    analytic empirical scaling has not been able to describe the full
    range of phenomenon observed in experiments. Thus the goal is to
    develop comprehensive transport models, based on more complete 3-D
    turbulence simulations and/or sound theoretical principles, with a
    minimum of (or no) empirically-determined adjustable parameters,
    that are accurate enough to compare well with past experiments and
    can be used to predict and optimize the performance of future
    experiments.