A. Cardinali

G. Giruzzi

K. McGuire

S. Bernabei

English

Crossref

PPPL-3244 - Preprint: March 1997, UC-420 
A Study of MHD Feedback Stabilization in 
Tokamaks with Lower Hybrid Waves 
S .  Bernabei, A. Cardinali*, G. Giruzzi# and K. McGuire 
Princeton Plasma Physics Laboratory, P. 0. Box 451, Princeton ,New Jersey 08543 
*Associazione Euratom-ENEA sulla Fusione, C.R. E. Frascuti, Italy 
#Rrsociation Euratom-CEA sur la Fusion, Centre d'Etudes de Cadarmhe, Frame 
Abstract. 
Lower Hybrid Current Drive (LHCD) has been succesfully employed in current profile control 
experiments and can be utilized to prevent MHD instabilities by tailoring the profile. Similarly, 
theory has shown that LHCD can be very effective in stabilizing MHD instabilities by feedback 
techniques: this experiment has not been tried yet. This paper addresses some of the practical 
aspects of such an experiment. 
INTRODUCTION 
Feedback stabilization of the m=2, n=l island with Lower Hybrid Current Drive 
has been theoretically proposed several years but never experimentally 
tried. Indeed, it has been often reported that in LHCD experiments, the m=2 mode 
was destabilized. This has been not because of any unique properties of LH waves 
that cause destabilization, but rather an indirect result of experimental requirements to 
date. So far, LHCD experiments have been designed to drive current efficiently, 
necessitating couplers which are able to launch the highest phase velocity waves 
compatible with accessibility; this has usually concentrated the rf-driven current 
inside q=2, thus steepening the current gradient at the rational surface. This is a way 
of destabilizing the m=2 mode.5 For plasmas with moderate electron temperature, a 
LHCD feedback stabilization experiment might therefore require a dedicated coupler 
able to launch slow waves which are absorbed in the outer region of the plasma. 
Feedback stabilization of the m=2 tearing mode can be effected by driving non- 
inductive current inside the magnetic island, in the same direction of the main current. 
A very attractive feature is that the stabilization is very rapid since it is caused by the 
reduction of the electric field which drives the mode: this is achieved with the back- 
emf induced by the non-inductive current.6 In contxast, current profile modifications 
require much longer times, of the order of the resistive time. 
Radial localization to a narrow region is not critical, provided that the driven 
current overlaps the island. The stabilization derives from the decrease of the electric 
field inside the island, so only the current which is localized inside is effective; the 
current which is deposited outside has only a minimal effect (provided it is not 
concentrated inside q=2). Therefore, the radial localization is not critical provided that 
the driven current overlaps the island. 
Poloidal localization is not essential either, since the effect is dominant at the 0- 
point: the current deposited at the X-point has relatively little effect.6 However, a 
major advantage of a modulated current derives from the fact that up to a factor of 5 
less current is required compared to a DC current.6 
DISCLAIMER 
This report was prepared as an account of work sponsored 
by an agency of the United States Government. Neither the 
United States Government nor any agency thereof, nor any 
of their employees, make any warranty, express or implied, 
or assumes any legal liability or responsibility for the 
accuracy, completeness, or usefulness of any information, 
apparatus, product, or process disclosed, or represents that 
its use would not infringe privately owned rights. Reference 
herein t o  any specific commercial product, process, or 
service by trade name, trademark, manufacturer, or 
otherwise does not necessarily constitute or imply its 
endorsement, recommendation, or favoring by the United 
States Government or any agency thereof. The views and 
opinions of authors expressed herein do not necessarily 
state or reflect those of the United States Government or 
any agency thereof. 
DISCLAIMER 
Portions of this document may be illegible 
in electronic image products. Images are 
produced from the best available original 
document. 
EXPERIMENTAL CONDITIONS FOR LHCD FEEDBACK 
STABILIZATION 
The main experimental challenge is to be able to locate the rf-induced current 
inside the island. The ray trajectory intercepts the island, since it has been shown 7 
that the perturbed magnetic field does not change appreciably the propagation of the 
LH waves; but it is practically impossible to rely on multiple passes of the waves 
through the plasma and rill upshift to "hit" the 0-point of the island, so it is necessary 
to have previous knowledge of the radial location of the island and damp the rf- 
waves in first-pass. ( S e e  figure 1) (In principle it is also possible not to depend on 
the knowlegde of the radial location and scan the phase of the grill in order to 
optimize nil, but as a proof-of-principle it is simpler to operate at a given rill 
throughout the pulse). 
wave Having to damp on first-pass has a 
consequence on the efficiency in 
moderate electron temperature 
experiments, because this requires 
launching moderately high rill. The 
current drive efficiency is also reduced 
from the fact that a high nil requires small 
waveguides, which limit the maximum 
power that can be transmitted with a 
single coupler. Because of these 
cosiderations it is essential to evaluate the 
necessary current and the time required 
As a reference, we take a D-shaped 
plasma9 with 660 kA of current and 15 
kG magnetic held on axis. 
Following the treatment of Morris? the threshold for the m=2 stabilization is 
found at approximately 15 kA of modulated current (compared to about 200 kA in 
case of steady-state current,and assuming the rf deposition to be =1/3 of the radius 
and the island width ~ 0 . 1  the radius). The stabilization time depends on how much 
the driven current is above the threshold.Very interestingly, it is expected to be a few 
milliseconds. 
Next it is necessary to phase the modulation so that the rf power is deposited 
inside the island: modulation of tens of kHz is well within the capability of any LH 
system and the driving signal can be obtained from Mirnov coils, BES or ECE. 
Since, as mentioned previously, the ray trajectory cannot be easily calculated easily in 
real time, a technique similar to that employed on Compass10 can be applied with the 
added feature that the timing of the modulation is varied until the m=2 signal is seen 
to decrease. 
It should be noted that, in situations in which the current drive efficiency is too 
low (due to the high nil-spectrum used), it is possible to increase it by making use of 
a compound spectrum: one coupler launches a high ql-spectrum which establishes a 
sup ra thed  tail, while another, launching a lower nil, increases the efficiency. In 
this scenario it might prove convenient to launch the high nil DC, in order to keep an 
electron tail continuously centered around the m=2 island, and modulate the second 
coupler (the main contributor to the rf current) in order to increase the current at the 
mode 
Fig. 1 Schematic of the LH for stabilization. 
wave trajectory and of the m=2 
magnetic island 
0-point. 
MODELLING 
An equilibrium modelling code with a LH ray tracing package11 has been used 
to determine the conditions required to perform an experiment in a plasma with the 
following characteristicsg: 
major radius e 1 6 0  cm 
aspect ratio A=3.38 
elongation ~ 1 . 5 8  
triangularity &=0.67 
pPol= 1.57 
magnetic field on axis Bp1.4 T 
plasma current Ip=660 KA 
safety factor on axis qe1.14 
q95=3.65 
From the magnetic equilibrium we find that y(q=2)=0.7 (corresponding to 
r/a=0.8) and that the electron temperature at this location is Te=1400 eV. 
In order to determine which nil-spectrum to launch, the damping location of 
individual values of 41 have been evaluated with the ray tracing package of the code: 
it is easy to show that a spectrum with 5.01n1115.5 is necessary to first-pass damp 
at Tez1400 eV. Such a rill-spectrum can be launched by an array of 32 waveguides, 
at the frequency of 4.6 GHz. 
The radial distribution of rf current density generated by such spectrum, carrying 
200 kW, is shown in figure 2.40 kA of current are generated near ~ = 0 . 7 ,  of which 
approximately 20 kA directly inside the magnetic island. Since the poloidal spread of 
the rf-current is A8=10°, the spatial resolution is more than sufficient for the 
feedback modulation stabilization scheme. Toroidal localization is not needed, since 
LH waves follow the field lines, but a calculated spread of Ap5"  illustrates well the 
localization of the damping. 
300 . . ' I . ' ' , . . .  1 . I . . .  It is interesting to note that a broadening 
250 ! \  I: of the launched spectrum (such as one 
c 2. RF deposition , - launched by an array of 16 waveguides) 
does not result in a broader power 
deposition, but mainly in a shift of the E h  
g Yloo t damping toward lower electron 
0 . . . # . . . I . . . {  ' Is..- "content" of large rill in the spectrum 
The necessity of a high number of 
waveguides derives from their 
narrowness, which implies lower power 
per waveguide (this limitation is largely 
removed in a machine Like ITER, 
because of the high electron 
temperature). 
Some spread of the rf current is caused by radial diffusion of the fast electrons: 
the very fact that high nil are used, insures that the effect of diffusion is minimal. 
Figure 3 (obtained by means of the 3D Fokker-Planck code of Ref.8) shows the rf 
current for different values of the diffusion coefficient Dp Another source of spread 
of the rf current could derive from the finite poloidal size of the coupler: ray tracing 
calculations show that the trajectories diverge somewhat only after the fmt pass 
through the plasma. 
- E 150 island w i y  \ j  \\
-g cu-200 
01 
\, - 
i - temperature. This is because the higher 3 50 
0 0.2 0.4 0.6 0.8 1 requires lower Te for damping. 
Y 
Fig.2 Calculated radial distribution 
of the rf current. 
CONCLUSIONS 
The practical feasibility of a feedback stabilization experiment using LHCD has 
been investigated. It is found that even in moderate temperature plasmas MHD 
instability can be stabilized by a modest amount of power: the principal requirement 
of the LHCD is the condition of first-pass damping. It is found that localization of the 
rf current and diffusion do not constitute a problem to the stabilization, which 
appears to be very fast. 
The relevance of demonstrating the 
stabilization of the m=2 mode with 
LHCD is obvious when we consider 
that such experiment would be much 
easier in a machine like ITER the much 
higher electron temperature in the 
vicinity of the mode and the much 
larger radius allow a far better 
localization and efficiency than in 
present tokamaks, without the need of 
0 0.2 0.4 0.6 0.8 1 using thin waveguides. A feedback 
stabilization with LHCD would be of r/a 
Fig. 3 RF current broadening due to great value, in comparison with an 
the fast electrons diffusion for 2 equivalent experiment with ECCD. In 
values of the diffusion coefficient Dr. fact, in the latter scheme, a somewhat 
better localization is balanced by a very 
low efficiency, especially in the outer 
portion of the plasma (owing to trapped electrons). It should also be noted that for 
ECCD, at a given magnetic field, the mode resonant surface should be tracked by 
mechanical movements of the mirrors which constitute the antenna. Conversely, for 
LH waves, the power deposition profile can be spatially shifted by changing the 
phase velocity of the waves (Le. by changing the phasing of the waveguides in the 
coupler). In a machine like ITER, this can be accomplished in real time. 
loo _ '  " I . ' .  1 ' * '  I "  ' 1 ' .  - ,  
D, = 0.7 m 21s - 
20 : 
AKNOWLEDGEMNTS 
This work was supported by the U.S. Department of Energy under contract No. 
AC02-76-CHO-3073. 
REFERENCES 
1 A. H. Reiman, Phys. Fluids 26 (3, (May 1983) p. 1338 
2 P. H. Rutherford, Basic Phys. Processes of Tor. Fus. PZsamus, Varenna (Italy) 
1985,2 p. 531 
3 D. W. Ignat, et al., Course and Workshop on Applications of RF Waves to 
Tokamak Plasmas, Varenna (Italy, 1985) 2,525. 
4Y. Yoshioka, S. Kinoshita and T. Kobayashi, Nucl. Fus. 24,565, (1984) 
5E. Westerhof, Nucl. Fus. 27, no. 11, (1987) p.1929 
6 A W Morris, R Fitzpatrick, T C Hender and M R O'Brien, 1992 Int. Con. on 
Plasma Physics, Innsbruck 1992, (EPS Geneva) vol. 16C part I p. 423 
7F. Romanelli, A. Cardinali and R. Bartiromo, Phys. Fluids Bl(8) (1989) p. 1659 
8 G. Giruzzi, Plamsa Phys. Contr. Fusion 35, A123 (1993) 
9 FSX report, to be submitted as a PPPL report. 
1oG. J. McArdle, A. M. Edwards, B. Lloyd, A. W. Morris, P. R. Simpson and G. 
A. Whitehurst, Proceedings of the EC-9 Workshop, 271-283 (Borrego Springs, 
California, January 1995) 
11 A. Cardinali, ENEA report to be published. 
DISCLAIMER 
This report was prepared as an account of work sponsored by an agency of the United States 
Government. Neither the United States Government nor any agency thereof, nor any of their 
employees, makes any warranty, express or implied, or assumes any legal liability or responsi- 
bility for the accuracy, completeness, or usefulness of any information, apparatus, product, or 
process disclosed, or represents that its use would not infringe privately owned rights. Refer- 
ence herein to any specific commercial product, process, or service by trade name, trademark, 
manufacturer, or otherwise does not necessarily constitute or imply its endorsement, ream- 
mendation, or favoring by the United States Government or any agency thermf. The views 
and opinions of authors expressed herein do not necessarily state or reflect those of the 
United States Government or any agency thereof. 


A study of MHD feedback stabilization in tokamaks with lower hybrid waves

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A study of MHD feedback stabilization in tokamaks with lower hybrid waves

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