J. Plasma Fusion Res. SERIES, Vol.4 (2001) 180-188

A Prospect - Plasma Physics, quo vadis.
ITOH Kimitaka+
National Institute for Fusion Science, Toki 509-5292, Japan(Received: 5 December 2000 / Accepted: 5 October 2001)

Abstract
A prospect of plasma physics at the turn of new century is discussed. The theme of this conference
identifies the future direction of the research related with plasmas. Main issue is the potential andofstructure formation in plasmas; More specifically, structures which arc rcalized through the interaction
iselectromagnetic fields, in particular that with electric fields, in non-equilibrium state. An emphasis

as thatmade to clarify the fundamental physics aspects of the plasma physics in fusion research as wellofin the basic research of plasmas. The plasma physics will give important contribution to the solution
showingandHaving an impact on human recognition of nature
the historical enigma, i.e., all thingflow.

a beauty in a law, the plasma physics/science will demonstrate to be a high-quality sciencein the 2lst

century.

1. Introduction
The llth International Toki Conference isprospect stimulates readers to access various revlew
articles in order to search thorough descriptions oforganized at the end of the 20th century, focusing on therelated work.

subject of potential and structure. It shows the

2. Beginning of Physics of the 20th Century
and Theme of This Conference

achievement where the plasma physics of 20th century
has reached, at least in the area of conference topics'
Therefore the prospect, which is given at the end of thisconference, might imply to provide a perspective of the

When one think about the new century, it isworthwhile to look back how the physics of 20th
century has begun. It is well known that Lord Kelvindescribed the status of the physics of that time as "Thebeauty and cleamess of dynamical theory is obscured by
two clouds". These two clouds are the remaining enigma

plasma physics in the 2lst century. In the following, anemphasis is made to clarify the fundamental physics
aspects of the plasma physics in fusion research as wellas those in the basic research of plasmas**.
In some of preceding conferences Il], couples ofprospects have been presented' In this prospect, it isat that time, i.e.,(1) Motion of the earth through elastic ether(2) Anomaly of the specific heat ratio of theintended not to repeat previous ones, owing to the limitof allocated time in the programme. Summarizing thisconference is not in the scope of this presentation as
well; examples here is limited and might be biased'materials which are composed of molecules.
The specific heat ratio did not agree with the calculation

based on the equi-partition law and the Boltzmann
statistics. The solutions of these two problems were
given by the progresses in the theory ofrelativity and in
the quantum physics. It turned out clear that this is theSuch shortcomings would be compensated' if this**It is also noted that some of readers might use words

area where the most picturesque evolution of the physics'plasma science' to describe what is called 'plasma physics'
in this article. No strong discrimination is intended hereof 20th century has been made. If the matter is in the

between these two Phrasings.
*

C o r r e s p ondin

I@2001 by The Japan Society of Plasma
Science and Nuclear Fusion Researchautho r' s e -mail : it oh @ nifs. ac.j p

180Itoh K., A Prospect - Plasma physics, quo vadis.

thermodynamical equilibrium, its property can be

Structure and turbulence
Statistical physics

precisely calculated, in present days, by use ofthe equi-partition law with Hamiltonian described by quantum

Ineversibility, chaos and control

theory.

Symmetry
Momentum transport
Improved confinement
Synergy of research methods

At the turn of the 2lst century, it has become
increasingly clear that only very limited part of ouruniverse is in/near thermodynamical equilibrium.

Almost all in the universe, of which we have empirical

Finally, closing is made discussing Exploring plasma

knowledge, is far-away from the thermodynamical

physics.

equilibrium, full of dynamics that generates structure,

Readers might stress other important issues in theplasma physics in the 2lst century. For instance, theand in the plasma state. One of the central issue of thephysics in the new century is to investigate the law thatgoverns the plasmas in nonequilibrium state.

energy release induced by the change of topology, theabrupt change of topology, the acceleration of selective
particles, the nonequilibrium atomic and nuclear physics
in the plasma state, the gravitational interactions, thegluon plasmas, the matter-antimatter plasmas, etc., are

The theme of this conference clearly identifies the
future direction of the research related with plasmas.

Main issue of the theme is the potential and structureformation in plasmas. Structures which are rcalized
through the interaction of electromagnetic fields, inthe challenging subjects for the human recognition of
the nature. These important issues are not addressed,
because this prospect is discussed along the main
subject of this International Toki Conference.

particular that with the electric fields, in non-equilibrium

state. This is schematically shown in Fig. 1. In thisfigure, the word 'microscopic structure' means that thefocus is placed on the range of the scale length ofinteraction between particles or elements: (Organized
form could be realized in much wider region than thecharacteristic scale length of binary interactions.) The'macroscopic' implies that the scale length of concern(e.g., inhomogeneity) is much longer than that of thebinary interactions. Combination of the magnitude of thecoupling (often represented by the plasma parameter f

3. Structure and Turbulence
One of the main issues is the law of mutual
regulation between the global (or mesoscale) structures
and turbulence. It has been well known that(1) turbulence destroys structures.
This has often been discussed in conjunction with the=llnlf,) and the distance away from the thermodynamical

equilibrium provides the variety in the spatial structure
and temporal evolution of plasmas.
In the following, a prospect is discussed, choosine
kevwords ofI;F,MicroStructures

Macroscoplc

Structures

Gradient

Fig.2 An example of Karman-vortex-like structure inclouds. Clouds near Kyushu island are shown.
(Ouoted from [2]).

Fig. 1 Direction of research on structures in plasmas

181

ltoh K., A Prospect - Plasma physics, quo vadis.

plasma confinement in toroidal devices. Anomaloustransport, which is considered to be induced by theplasma turbulence caused by various instabilities, limits
the energy and particle confinement times in toroidal
plasmas. In the fusion-related research using toroidal
plasmas, the suppression of turbulence has been themain problem in order to make confinement time longer.
It should be emphasized, at the same time, that(2) turbulence generates structures, and that(3) it is accompanied by transitions.
In reality, many examples of structure, which weobserve in daily life, in laboratory experiments and inthat tremendously enhances the viscosity. Other famous
example is the geodynamo. The turbulence, driven by
the heat source, in the conducting fluid generates the
structured magnetic field' In a system where turbulence
generates structure, transitions take place.

These mutual regulations of structure andturbulence are ubiquitous for plasmas away fromthermodynamical equilibrium, and is a main theme of
the modern plasma physics. Within the theme of thisInternational Toki Conference, a key issue is the fact
that(4) the electric field has a profound impact on theobservatories, are sustained by the presence ofstructural generation.
One of the most familiar example that the radial
electric field plays an essential role in sustaining thestructure is a bubble of soaped water. (Fig. 3)' The
radial electric field is generated near the surface' The

turbulence. If one chooses an example frommeteorological observations, a Karman-vortex-likestructure of clouds is often found. (See Fig' 2)' Karmanvortex appears in the range of the Reynolds number
about 100. The system of air and water vapor in Fig. 2

electric field directs inward on the outer surface, andoutward on the inner surface. These two layers ofradial

has extremely large Reynolds number, and theobservable structure is possible owing to the turbulenceElectrostatico5F'Fig. 3 Radial electric field in a bubble. Bubble (a) andschematic drawing of the radial electric field (b)'Polymers are aligned normal to the surface' One
end of the polymer is positively ionized: this end
is much more solvable to oils, not to water' Theooother end the polymer is negatively charged: thisend is akin to water. Electric field normal to the

0.5

Fig. 4 Potential structure, plasma temperature andfluctuations. (Ouoted from [3].)surface is generated near the surface.

r82

Itoh K., A Prospect - plasma physics, quo vadis

InterfaceE,

Efnn"'

A,
6*"ro

B

Streamerf int

Fig. 5 Radial structure of the electric field domain interface (a).
Zonal flow (b) and streamer (c) are illustrated on thepoloidal cross-section.

electric field are repulsive. As a result of this repulsive

interaction, a local deformation which changes the
thickness of the bubble is restored. The bubble is stableagainst the perturbation that leads an irregularity inthickness. Owing to this stability, a bubble can survive

very long time (until water molecules are lost by, e.g.,
evaporation).

A stability owing to the radial electric fieldstructure has also been studied very intensively inmagnetized plasmas. Role of the radial electric field in
the improved confinement phenomena in fusion research
Fig. 6 Mutual regulations of microscopic fluctuations
and mesoscale structures.

is discussed later ($8). The importance of the meso_scale
structure of the electrostatic potential is recognized morestrongly. Examples of such structures are quoted fromCHS experiments. (Fig. 4). A particular structure of thethe domain interface and zonal flow suppress theturbulence while the streamer can further excite

radial electric field is now known essential indetermining the level of turbulence and transport.

instabilities. (Fig. 6). Detailed explanations are given in

There has been a substantial progress inreviews, e.C., [4). Through these nonlinear links, aunderstanding of the turbulence and turbulent transpon.

turbulent state self-regulates. Fluctuations are in many

In a dimensional argument of turbulent transport, thecases driven by nonlinear instability mechanisms, not by

turbulent transport coefficient is estimated by a relation

linear instability mechanisms. Turbulent state is often

realized through the subcritical excitation. Thus

D=Tl2

turbulent states evolve accompanying transitions. The

where 7is the decorrelation rate and I is a decorrelation
length of fluctuating motion of plasma elements. Whenthe turbulence is induced by instabilities, a conventionaltransitions are characterized by the autocorrelation timeof fluctuations and mesoscale dynamics. Therefore it
can take place in a much shorter time in comparison

picture is to estimate y and (, by the growth rate y, and,with the gradual evolution of global plasma parameters.

wave length ft;t of the linear instability mode, obtaining

This is a key in understanding the fact that abruptchanges of state (symmetry, noise level, transport

D = h k'|. This turns our to be over simplified [4]. In astrong turbulent state, the decorrelation time and length
are strongly influenced by the mesoscale structures (incoefficients, etc.) have been commonly observed in thelaboratory plasmas as well as in space and astro
plasmas. This understanding forms a basis for future
investigations of turbulent phenomena in general.

particular that of the electric field). Typical examples ofthe mesoscale structures are the electric field domaininterface, zonal flow and streamer. (Fig. 5). Nonlinear
interactions cause complicated relations; the turbulent

4. Statistical Physics

modes can generate or destroy mesoscale structure, andIf the equipartition law holds, the property of183

Itoh K., A Prospect - Plasma physics, quo vadis'

plasmas, in principle, could be derived by explicitly

calculating collective modes or particle interactions'However, it is satisfied only in a limited case, andmajority of plasmas are away from thermodynamical
equilibrium. Example in $3 belongs to typical cases:
turbulent states do not satisfy the equipartition law' For

a set of quasi-two-dimensional fluctuations, theequipartition law predicts E1,* (fuT)k1, where fp is theenergy density of the mode. For turbulent fluctuations,different power laws, e'g', E* * fti3' have been derived'
and magnitude is extremely larger than Ep* (kBT)kL[4]. Deviation from simple statistical law has also been

entropy. As an example, Tsallis statistics is well known[5]. In Tsallis statistics, an extended 'entropy' is nolonger extensive quantity. So far, it is recognized that

the Tsallis entropy seems to capture some essential
elements of turbulence, and that the structure of the nonneutral plasma might be explained better by employing
such new statistics.

In a far nonequilibrium plasmas, turbulent

fluctuations are associated with a large degree of
freedom, and a result for particular case (e'g', E** kI3
for drift wave range instabilities) must be generalized asa law of statistical theory. Efforts in this direction havealso been elaborated. Method of renormalization allows
to separate nonlinear interactions into coherent drag andconfirmed in experiments. Observed probability density
function of local fluctuation-induced flux deviates fromGaussian distribution, and contribution from rare but
large-amplitude pulses has considerable impacts. (Morenonlinear self-noise excitation [6]' Based on this, itcame to a point that a working hypothesis is proposed:
statistics of turbulent modes could be described by thebasically, inhomogeneous systems are not extensive:

renormalized dissipation function 5(c)' (Fig. 7 [7]) It is

When there are two inhomogeneous systems of the same
temperature, the internal energy of combined system(A+B) is not necessarily equal to the sum of those of A

another generalization of Boltzmann's entropy, andrecovers Prigogine's entropy production rate as alimiting form as well. A minimum principle is proposedby use of function 5(E). Power law statistics in theand B. The extensiveness is one of the basis ofconventional statistical physics') A framework of theprobability density function and in transition probability
are obtained. The power index is dependent on theinhomogeneity (i.e., the magnitude of non-equilibrium
deviations): This dependence might be a newstatistical physics, which is beyond the present
nonequilibrium statistical physics (Boltzmann-FermiBose statistics, Kubo formula, Prigogine's principle forminimum entropy production rate, etc.) is necessary'
In some cases (e.g., non-neutral plasmas), plasmas'universality' in far-non-equilibrium systems'

remain in a thermodynamical equilibrium state'

5. lrreversibility, Ghaos and Control

However, the extensiveness is not necessarily
guaranteed. Therefore, even if plasmas are inthermodynamical equilibrium, the conventional

The statistical theory is based on understanding of
the irreversibility. The above-mentioned extension of
statistical theory provides an H-theorem, that the accessto the steady-state turbulent solution occurs. This access
is observed as irreversibility, and the origin of thestatistical theory may not be sufficient. One formal wayof the statistical theory is to extend the definition of theirreversibility has been one of the key issues in the

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Fig.8 Lyapunov exponents of electron motion tn

Fig. 7 Renormalized dissipation function as a function of
the fluctuation level. (Schematic, quoted from [7]')homogeneous plasmas. (Quoted from [8].)184Itoh K., A Prospect - Plasma physics, quo vadis.

physics. At the beginning of this cenrury, theplasma physics has advantages. The selection rule ofirreversibility is placed on the Boltzmann's Stosszahl
Ansatz'. Now the origin is understood in terms of the
Lyapunov exponent of the dynamical motions. The

symmetry and dynamics of strong coupling systems canalso be studied by use of dust plasmas. One
characteristic feature of dust plasma is that the larger
charges ofparticles make the scale length longer. (Ikezi[ 1]). From this reason, the change of symmetry, suchas 'melting' and change of crystal lattice, is observed inlaboratory with a characteristic scale length like mm.
This should be compared with the scale length of solidstate where inter-particle distance is of the order of lG_
100A. This means rhat the plasma physics has aninnovative microscope (e.g., order 10s) in investigating
the dynamics of interactions that drive a symmetry in ascale much longer than the binary interactions. Relatedwith this, the nonequilibrium character of the charge ofdust will also be illuminated by the light of turbulenceand structure formation. Formation and destruction ofsymmetric structure have also been discussed forplasma theory has advanced to quantify the Lyapunov
exponents in plasma interactions. (Example is shown in
Fig. 8) The irreversibility in plasmas is becoming muchclearer. In parallel with the understanding of the natureof chaos in plasma dynamics, the control of chaos isanother important issue in plasma physics. A couple ofreports have been made these days.

In physics (and more general sciences), understanding is achieved in efforts of trying to control
the object. The irreversibility in thermodynamics,
formulated as the second law of thermodynamics, hasbeen investigated by employing the Gedankenexperiment of 'Maxwell's demon' (1870) t9l. It is now
clear that the Maxwell's demon does not work. In
observing the velocity of each particle by use of (say)charged polimers [12].

light, Demon's temperature is increased. When the

Other subject of the symmetry is found in thetemperature becomes high, the Demon is subject to therandom motion which is in proportion to temperature.

transport problem. In the classical statistical physics, theCurie's principle is established. That is, the flows ofWithout being cooled, the Demon cannot continue roscalar quantities (say, particle number density or internalenergy) do not interfere those of vector quantities (say,select proper particles.

Looking back the Maxwell's Demon, one sees amomentum or angular momentum). This principle isdeduced from the consideration of the symmetry. In

key issue in the control of chaos. The issue is anecessity of information and power in controlling achaos. Others are, e.g., how one control the turbulence
in which a large degree of freedoms with positive
Lyapunov exponents, or whether the structure could bemanipulated by the control of chaos. Understanding of
the origin of irreversibility would be followed by theinvestigation to find a law behind various observations
and present controlling experiments.

thermodynamical equilibrium, the momentum flux is notcaused by the gradient of pressure. This kind ofprinciple must be investigated in plasmas. It is ofinterest what law is established in a non-neutral plasmas

which can be near the thermodynamical equilibrium. In

magnetic confinement devices, turbulence often

6. Symmetry
Investigation of the selection rule of the symmetry

is another majour issue in modern physics. In a strong
coupling plasmas, detailed study has been in progress.
An example might be seen in a phase diagram of thehydrogen (the simplest atom). (Fig. 9) In a very highSolid state hydrogen(Molecular)

6
Il

Critical point forplasma phase tjans.

E

:

o
o

density region, the metal hydrogen is predicted, and thetransition between plasma and liquid metal is studied.
More variety of matter and states will be investigated in

o

i!o

g**i

E

o-

the future along this line of plasma physics. The
selection rule of symmetry among gas, liquid, solid andcrystal has been investigated.
For uch a research area, the solid state physics and

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E

E

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103

104

10s

Temperature (K)condensed matter physics have been contributing
together with plasma physics. In this direction, the105

Fig. 9 Phase diagram of the hydrogen (Ouoted from
Ito11

185

ltoh K., A Prospect - Plasma physics, quo vadis.

un-identified 'dark-matter' still occupies the majority ofthe speculated total mass of this cosmos, the role of thedominates the cross-field transport. In this case, thesymmetry of the system is spontaneously violated byturbulence, and the Curie's principle does not hold. It

magnetic field energy should not be underestimated.
One example might be considered in conjunction withthe future of this cosmos. If the total energy of theuniverse is negative, the universe which is now

has also been identified, that the momentum flow can be

induced by the temperature gradient in tokamak
experiments [3].

expanding with the present Hubble constant will start toshrink again. In a final state the gravitational force

7. Momentum TransPort
The law of momentum transport has profound
impact on our understanding of the universe. In thecauses the collapse. The rate of collapse should be
influenced strongly by the presence of magnetic field.
The magnetic energy resists against collapse if thegravitational system like our galaxy and universe, thegravitational energy is released as kinetic (or photonic)

magnetic flux is conserved. The rate of the flux
annihilation, which is solely determined by the plasmaenergy through the exchange of momentum andmomentum transport. When the angular momentum ofsome element, which is captured by the gravitational

dynamics, enters as a mechanism that dictates the time
rate of evolution.

central force, is conserved, the gravitational energy is

8. lmproved Confinement

not released. Once the exchange of angular momentum
takes place between many elements in this gravitational
system, some elements start to fall down so that the total

The issues of the turbulence transition, mesoscale
dynamics, momentum transport and irreversibility' havealso been investigated in the context of understanding of
the improved confinement. In the area of magnetic
confinement research of plasmas, the problem of the
improved confinement played a strong driving force forthe evolution of the plasma physics' After the finding of

kinetic energy is released. Understating of the evolutionof astrophysical objects (accretion disks, active galactic
nuclei, etc.) will be promoted by the progress ofunderstanding of the transport of angular momentum
through interaction of plasmas and electromagnetic

the H-mode by Wagner and collaborators on ASDEX
tokamak in 1982 [15], we had now two decades offields. The dynamo physics is also an important elementin this subject. (Fig. l0)
Change of angular momentum includes thegeneration of magnetic field through plasma dynamics.

research.

The finding of the H-mode has opened a new world
for plasma confinement research, and many improved
confinement modes have been found later. Some
examples are listed as follows: CNTR-NBI mode, Core

One of the most famous problems is the origin ofgeodynamo. In addition, the generation of the large
scale magnetic field could have a strong influence tomodify our view of the cosmology. It is now becoming
clear that substantial part of the astrophysical energy isstored in a form of the magnetic energy [14]. While the

H-mode, ERS-mode, Helical system ITB, High-p, Hmode, High-Bo mode, High-1, mode, High Ti H-mode,
High Zi mode, HIT mode, Il-mode, I-mode, IOC' LHmode, Pellet mode, PEP H-mode, RIM, Supershot, VHmode, Z-mode (Alphabetical order: It is not exhaustive.)

Improved confinement modes had profound impact
on fusion research. For instance, the design study of thefusion experimental reactor has shown that the cost of
the device follows an empirical fitting
C e l!-r'3

where C is a cost and F1 is an enhancement factor of theenergy confinement time over the L-mode scaling [16].

The finding of the H-mode made the fusion
experimental reactor realistic.
In addition to this impact on fusion research, the Hmode and following series of improved confinement

modes have propelled the plasma physics of hightemperature plasmas. Many elements of progress beyond

Fig.10 A model of accretion disk (quoted from [4]).
186

ltoh K., A Prospect - Plasma physics, quo vadis

the quasi-linear theory of turbulence, have been(a) 5ooM

explored being motivated by the H-mode phenomena.
As is discussed in 93, the role ofthe radial electric field300

structure has been understood in the efforts to study themechanism of the H-mode. Subsequently, the mutual
regulating features of turbulence and potential structures
have attracted interests of plasma physicist. present

€
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E

to0

working hypotheses, being initiated by S-I Itoh, Shaing,oDiamond, and coworkers, is the transition of turbulence-100

coupled by the mesoscale electric structure. This is

widely accepted, and a lot of efforts are done in thisdirection. (For a theoretical review, see, e.g., [4,17] andfor experimental ones, see, e.g., t181.) It must be
stressed, however, a direct confirmation of the causality

(b)

E /E*
1.5

has not yet been established. The time and spatial scaleof transition is not yet been fully understood. Further
breakthrough is still looked for. Similarly, there aremany un-explained peculiar phenomena in toroidal
confinement: the origin of particle pinch, the transient

rr

0.5

response of profile against change of external
conditions, the sudden occurrence of collapses, etc.
Understanding of these phenomena, if obtained, will
give an insight into the general mechanism of structuralformation in the universe.

-5
(c)

51

10

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a
o
ct

9. Synergy of MethodologytoIn search of the breakthrough of the physics of thestructural formation in plasmas and the role of thespotential, one must also be keen about the methodology

tr|*of the study. It should be emphasized that the synergy ofphysics methods must be intentionally pursued. As thephysics methods, we have experimental, theoretical andcomputational methods. These three dimensions ofmethods are complementary each other. Uniting
research ofthese methods, one could think ofthe future

Fig.11 Bifurcation to solitary radial electric field nearplasma edge induced by the biased limiter.
Experimental result [19], theory [20] and Monte
Carlo simulation [21].

progress.

Let us take here one example: Divertor bias andbifurcation of electric freld. Experiments on TEXTOR
has identified that the radial electric field near plasma

Numerical simulation can treat a full expression of
nonlinear interactions, and yields quantitative result.
Understanding of the potential and structure formation
could be advanced by the synergy of the researchsurface is subject to bifurcation. If the applied voltage
exceeds a threshold value, there appear a solitary radial

electric field. This phenomenon is explained by theory.
By considering the nonlinearlity in the relation between

methods.

the radial current and radial electric field, "/,[E"], thesolitary electric field is shown to exist. Finally, thenonlinear simulation has shown that the bifurcation to
the solitary radial electric field can occur. (Fig. I l) The
experimonts provide the finding of events and control.
Theory gives modelling and understanding of themechanism, so that a scaling property is clarified.

10. Exploring Future Plasma Physics
In this article, a perspective is discussed for the
future of the plasma physics in the area of the theme ofthis International Toki Conference. After reviewing thefuture direction of research, one comes back to aquestion Why we are proud of plasma physics? The
reason is that the plasma physics is a high-quality and187

Itoh K., A Prospect - Plasma physics, quo vadis.

challenging area of science. In concluding so, it isReferences

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l Impact on human recognition of nature
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International Toki Conference are acknowledged. In
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Fig. 12 Historical problem for human recognition of
dynamics of the universe.

188