I. Physics Investigation

> The physics studies for NSTX have covered the areas of achievable
> shapes, confinement and transport, MHD stability, heating and current
> drive, and possible operational scenarios.

A. Confinement and Performance

> Operation in START has suggested interesting possibilities for
> enhanced confinement operation at low aspect ratio. In particular, the
> START confinement data seem to agree well with some popular L-mode
> scalings, most notably the Lackner-Gottardi scaling. This scaling has
> parametric dependences generally similar to those of ITER89-P, the
> more accepted L-mode scaling expression. As little is known about
> confinement scaling at low aspect ratio, an experiment such as NSTX is
> essential for determining the confinement characteristics at low R/a.
>
> The expected behavior of drift-type instabilities was studied using a
> comprehensive kinetic toroidal microinstability code which takes into
> account high-n effects, all resonances, finite beta effects, and
> finite-Larmor-radius and banana orbit effects. The study was performed
> in the electrostatic limit for plasmas at fixed q and RBt, over the
> range of aspect ratio from 1.25 to 2.5. The results indicated a
> reduction in the orbit-averaged curvature function (the instability
> drive), with decreasing aspect ratio, with the linear growth rate of
> the mode becoming negative (stability) for R/a ≤ 1.5. The effect is
> more pronounced in the more collisionless plasmas, again indicating
> the need for high power heating to achieve low collisionality. The
> ability to produce low collisionality plasmas with strong auxiliary
> heating as well as the ability to operate over a range of aspect ratio
> allows NSTX to explore the benefit of low aspect ratio in suppressing
> transport-inducing microinstabilities.
>
> A more general approach can be taken to assessing the variation in
> performance with aspect ratio. Various performance indicators can be
> formulated as functions of aspect ratio only with an appropriate
> number of constraints. For this exercise, one natural choice of
> constraints is fixed TF coil current density, βn, qedge, and Pinput.
> Given these constraints, the variation in confinement (ITER89-P
> scaling), β, Pfusion/Pcenter (the fusion power production normalized
> by the power dissipated in the center stack), and the (inverse) TF
> field utilization with aspect ratio is shown in Figure 2. What is
> plotted in the figure are normalized values (normalized to 1 at
> R/a\~1.5). It is the magnitude of the variation with aspect ratio that
> is important to note, and for this, the various parameters not only
> increase with decreasing aspect ratio, but the rate of increasing
> performance actually increases as the aspect ratio decreases,
> indicating large performance gains in the ultra-low-aspect-ratio
> region (R/a\<1.3). The TF field utilization factor, Ip/ITF, indicates
> the amount of TF that needs to be supplied; lower TF requirements are
> necessary with increasing TF utilization (decreasing ITF/Ip).
>
> The performance of low aspect ratio devices, based on the energetics
> calculations shown here, indicate that ultra-low-aspect-ratio is a
> promising approach for a compact Volumetric Neutron Source and/or
> reactor. Performance increases with decreasing aspect ratio, low R/a
> devices have only modest TF requirements, meaning that standard Cu
> coils could be envisaged, and studies have shown potential factor of
> two decreases in capital cost and COE over conventional fusion
> reactors, making an ULART reactor competitive with fission reactor
> COE.
>
> There are, however, several issues that need to be addresses for the
> development of a steady-state spherical torus reactor, most notably
> MHD stability and Current Drive.

B. MHD Stability and Beta Limit

> In order for a compact spherical torus reactor to be attractive, it
> must necessarily operate at high beta, with beta values typically \>
> 30%. Because of this, MHD stability is a key issue for
> ultra-low-aspect-ratio. Here, we examine the MHD stability for
> \"conventional\" pressure and current profiles with and without a
> conducting wall. Without a wall, the ULART stability is limited by
> low-n modes, with a β-limit of only near 25% (βn = 4). The low-n modes
> are effectively suppressed with the presence of a wall, as shown in
> the upper curve where it is now high-n ballooning that is the
> β-limiting factor. With the wall, the βt increases to approximately
> 33% (βn \> 5).
>
> An even higher βt value is obtained with profile optimization. This is
> shown in Fig. 3. The results of this profile optimization show two
> main elements. The first is that by raising q0 to \~3.4, the
> ballooning limit is raised to approximately 43% (βn = 8.7). Of crucial
> importance in this case as well as the previous one is the presence of
> the conducting wall, which effectively stabilizes the low-n modes once
> again. The other key feature of this profile optimization is the large
> amount of current carried by the bootstrap and diamagnetic currents,
> with 77% of the current due to bootstrap, this value increasing to 85%
> of the total current when other pressure gradient dependent currents
> are also considered. This self-driven current is of great importance
> for reactor operation without an OH solenoid.

C. Heating and Current Drive

> A spherical torus reactor design precludes an OH solenoid for two
> essential reasons. The first is that the center stack must be made as
> skinny as possible to minimize aspect ratio. The second is the neutron
> damage on insulating materials that would inevitably occur. In
> addition to these, a compact spherical torus reactor requires high
> current, typically 20 to 30 MA. These reasons make non-inductive
> current drive an essential element of an ST reactor. The non-inductive
> current drive can come from four sources; neutral beams, helicity
> injection, RF, and bootstrap current. The bootstrap current, which can
> account for up to 85% of the total current, was discussed in the last
> section.
>
> 1\. Neutral Beam Injection - Neutral beam current drive has been
> estimated for 5 MW of near-tangential injection into a low aspect
> ratio configuration. With Do ⇒ D+ injection and the temperature
> typical of NBI at the 5 MW level, Te(0) = 2.5 keV and Ti(0) = 5 keV,
> we find that about half of the fast ions are trapped at these low
> aspect ratios, and these, therefore, do not contribute to the current.
> The remaining passing particles impart enough momentum to electrons to
> drive approximately 0.3 MA of current. While this is not enough to
> sustain the 1 MA current fully non-inductively, it can play a
> significant role together with a high bootstrap fraction.
>
> 2\. Helicity Injection (HI) - This technique has been demonstrated on
> the HIT device at plasma current up to 200 kA. It can be extended to 1
> MA for use in the current initiation phase of NSTX, and HI may also be
> a viable technique to control the edge plasma current density during
> steady state.
>
> 3\. High Harmonic Fast Wave - The NSTX plasmas present special
> challenges for radio-frequency heating and current drive, noting that
> the plasma dielectric constant ωpe2/ωce2 is about 45 for typical NSTX
> parameters (this value is ≈ 1 for conventional tokamak plasmas.). At
> this value of ωpe2/ωce2, both Lower Hybrid and Electron Cyclotron
> waves have severe accessibility problems. Lower Hybrid accessibility
> is limited to high n\|\| (\>10), meaning interaction between the waves
> and low energy electrons, limiting the amount of possible current
> drive to an almost negligible value. There is virtually no access for
> Electron Cyclotron wave propagation for this value of the dielectric
> constant. (Recent theoretical calculations indicate that accessibility
> for ECH may be greatly improved using mode-conversion to electron
> Bernstein waves.)
>
> An intriguing candidate for RF heating and current drive is High
> Harmonic Fast Wave (HHFW). HHFW shows strong, single pass absorption
> for high-β operation, consistent with the high density, low TF regime
> of NSTX. The wave absorption scales as ne/BT3. Fast Waves have good
> accessibility up to βi values of \~ 50%, at which point the waves mode
> convert to the Ion Bernstein branch. The advantage of the Fast Waves
> is that their electron heating can lead to higher bootstrap fractions,
> and the power deposition can be localized for current profile control.
> It is estimated that between 0.2 and 0.9 MA of current can be driven
> by Fast Waves in NSTX equilibria.

The following summarizes the advantages for using HHFW for NSTX:

(a). Strong single pass absorption (90 -- 100%), Im k⊥ ∝ ne/B3 ∝ β /B.

\(b\) FW Electron Heating synergistic with advanced ST regime.

• Higher neTe and lower ν\* ⇒ higher bootstrap current.

• Higher Te ⇒ higher current drive efficiency.

• Localized heating and current drive ⇒ j profile control.

(c). Due to strong absorption, the current drive efficiency can be high.

• ICD(MA) ≈ 6 Prf(MW) ne-1(1013cm-3) R(m)-1 nˆ-2.

e.g., NSTX High Beta - 80% Bootstrap Fraction Discharges:

ne(0) ≈ 5 x 1013cm-3, R = 0.8 m, Prf = 7.5 MW.

Central CD (nˆ = 4): ICD(MA) ≈ 700 kA.

Off-axis CD (nˆ = 6): ICD(MA) ≈ 300 kA.

> (d). Good wave accessibility (ion beta limit of ≈ 50 % and no electron
> beta limit).
>
> (e). High power, long-pulse transmitters available at PPPL (7.5 MW, 5
> sec).

D. NSTX Operational Scenarios

> The attractive features of high-beta/high confinement and potential
> for fully non-inductive current drive are combined in NSTX for a
> MA-level proof-of-principle ST physics experiment. The tokamak
> simulation code (TSC) was used to model NSTX discharge start-up and
> maintenance, with an aim toward producing a fully non-inductively
> current driven discharge. For this case, a 0.5 MA target plasma was
> produced using the OH capability that is built into the NSTX solenoid,
> but the OH current is brought to zero, and maintained at zero once the
> current flattop (1 MA) is reached 0.2 sec into the discharge. A HHFW
> power of 5 MW is turned on and
>
> maintained once the plasma has reached the 0.5 MA target level. The
> HHFW power deposition profile is parameterized as a function of
> poloidal flux, Ψ, based on results from a slab, wave-damping
> calculation, with an additional 1-Ψ falloff to take into account the
> amount of trapped electrons that do not contribute to the current.
>
> Figure 4 shows the first 0.5 sec of time evolution for an NSTX
> discharge with HHFW current drive. The 0.5 MA target plasma has a
> relatively low electron temperature, Te(0)\~0.5 keV. Therefore, when
> the HHFW heating and current drive is turned on at this time, on
> average about 0.5 MA of current is driven. Later in time, the
> bootstrap current becomes more important reaching for this case to be
> 50%. Therefore, with HHFW and bootstrap current, it is possible to
> drive the entire 1 MA current. In the bottom panel of Figure 4 is
> shown the resistive surface voltage. Note that although the HHFW and
> bootstrap account for the total 1 MA current, there is still some
> residual positive resistive voltage; this is because the discharge has
> not settled down to a steady-state. The total current profile is not
> well-aligned with those of the bootstrap and Fast Wave profiles, and
> some voltage is therefore needed to effect this alignment. This
> indicates that some form of plasma profile control may be needed to
> optimize the bootstrap current fraction. The combination of core
> current drive with NBI (an upgrade option), profile control current
> drive via HHFW, and surface current drive via HI should make this
> possible.

E. NSTX Physics Summary

> From above theoretical investigations, the most promising regime for
> spherical torus and so for NSTX is identified to be the ULART regime,
> R/a ≈ 1.25 with significant natural elongation of κ ≈ 2.2. Moreover,
> to be reactor relevant, a fully non-inductively sustained high β ST
> regime with a sufficiently long pulse length of \~5 sec must be
> demonstrated. From the theoretical investigations, it appears to be
> feasible to achieve a non-inductively sustained high-β (≤ 40 %) /
> high-bootstrap-fraction (≥ 80%) regime with helicity injection and
> high harmonic fast wave heating and current drive at the reactor
> relevant 1 MA level low collisionality plasmas These regimes have
> sufficient plasma density ( \> 3.5 x 1019 m-3) to ensure adequate
> divertor operation and plasma cleanliness. The NSTX model discharge is
> prototypical of the ones used for the high performance ST reactor
> studies. With this challenging physics goal in mind, the NSTX device
> is being designed for maximum flexibility and plasma accessibility in
> a cost effective way by utilizing existing facilities and
> infrastructure at PPPL. Due to the wide range of challenging physics
> issues, active national participations in the NSTX physics program is
> planned.

[Technical Progress]{.underline}

NSTX Physics Activities

> The Physics team has worked closely with the Engineering team to
> address the key physics issues that impact critical design items such
> as the center stack, PF coil system and associated power supply
> requirements, RF power systems, and plasma facing components.
> Equilibrium calculations for both the up-down symmetric (Double Null
> and Natural Divertor) and Single Null (for Coaxial Helicity Injection)
> configurations have defined the required positions and shapes of the
> PF1a and PF1b coils, along with
>
> the coil current levels required to produce the range of possible
> plasma shapes. Furthermore, shaping requirements have been key in
> setting the height of the new OH solenoid. Calculations have been
> performed to determine the axisymmetric stray fields from such sources
> as the OH current during startup and induced eddy currents in the
> vessel and passive plates, TF leads, TF loops, and toroidal eddy
> currents induced in the TF center stack conductor due to ramping of
> the OH current. Only the first source of stray field (OH and eddy
> currents), was found to be significant. Calculations have been
> performed to determine the PF current levels required to compensate
> these stray fields and allow plasma initiation.
>
> Other areas in which Physics has contributed include Tokamak
> Simulation Code (TSC) scenario development for inductive plasma
> operation from near initiation to final OH current shut-down. This is
> important input into Engineering for determining the I2t heating of
> the various coils and the PF power supply voltage requirements.
> Results from these runs have also been used as input to RF coupling
> calculations to assess heating and current drive possibilities.
> Simulations in TSC and TRANSP have been carried out for Neutral Beam
> Injection scenario development, and this work is ongoing. The effect
> of the fast ion population on the RF heating of the plasma is also an
> area of ongoing work.
>
> TSC has been used to develop radial and vertical disruption scenarios;
> code output is used as a basis for determining stresses on the center
> stack due to induced and halo currents. Finally, 0D calculations have
> been used to estimate the expected heat loads on the center stack and
> divertor plates for all three plasma configurations. One and 2D heat
> flux calculations are underway.

[Future Accomplishments (i.e., FY97/98/99)]{.underline}