EFFECTIVENESS CONTOUR METHOD FOR EVALUATING COIL LOCATIONS FOR PASSIVE AND ACTIVE PLASMA STABILIZATION

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EFFECTIVENESS CONTOUR METHOD FOR EVALUATING COIL LOCATIONS FOR PASSIVE

AND ACTIVE PLASMA STABILIZATION

R. Thome, R. Pillsbury, Jr., W. Mann, W. Langton

To cite this version:

R. Thome, R. Pillsbury, Jr., W. Mann, W. Langton. EFFECTIVENESS CONTOUR METHOD FOR EVALUATING COIL LOCATIONS FOR PASSIVE AND ACTIVE PLASMA STABILIZATION.

Journal de Physique Colloques, 1984, 45 (C1), pp.C1-177-C1-180. �10.1051/jphyscol:1984136�. �jpa-

00223691�

J O U R N A L DE P H Y S I Q U E

Colloque C l , suppl6ment a u no 1, Tome 45, janvier 1984 page Cl-177

EFFECTIVENESS CONTOUR METHOD FOR EVALUATING C O I L LOCATIONS FOR PASSIVE AND ACTIVE PLASMA STABILIZATION

R . J .

Thome,

P i l l s b u r y ,

Mann and

Langton

Plasma Fusion Center, Massachusetts Institute of TeehnoZogy, U.S.A.

R5sumC - C e t t e p r e s e n t a t i o n d e c r i t une technique gCnErale pour p l a c e r

Elements passifs et les bobinages actifs dans la position la plus efficace pour stabiliser le mouvement vertical du plasma. Les profils gknkraux d'efficacitk sont indiquks, puis appliques au plan d'un tokamak particulier.

Abstract - A general technique is presented for placing the passive elements and active coils in the most effective postions for stabilizing vertical plasma motion. General contours of effectiveness are given and then applied t o a specific tokamak design.

INTRODUCTION

Vertical plasma motion is unstable in tokamaks with an elongated plasma since a negative field index is required. The radial field component is directed such t h a t the force on the plasma following a vertical displacement tends to increase the displacement.

Recent tokamak designs have considered separate control coils to provide active vertical stabi- lization of the plasma. An initial, rapid vertical plasma motion would be stabilized by eddy currents induced in passive elements; then, as the induced field decays, a set of active coils would be excited t o provide the required field. The power required for such control coils would be limited, since they would be excited only on the time scale of the induced field decay and not of the plasma motion.

The placement of passive elements and active coils to stabilize a vertical plasma motion is dependent on demands imposed by other subsystems. This paper presents general contours of constant effectiveness t h a t can be used t o estimate the relative merits of designs for both passive elements and active coils.

CONTOURS O F CONSTANT EFFECTIVENESS

The plasma is modeled as a single circular current filament of radius r, a t

with current Ip for t <

I t is assumed t o move instantaneously a distance Az a t t

0. Two passive coaxial loops of radius a are located a t

as shown in Fig. 1. At t

the plasma motion induces a

Fig. 1 - Plasma and Stabilization Loop Models in Real and Normalized Space.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984136

CI-178 JOURNAL

DE PHYSIQUE

current in the loops which in turn produces a restoring force due t o the radial field a t the plasma given by

where

is the permeability of free space;

tlr, is a dimensionless time;

= (L

M ) / R , where L is the self-inductance of a loop, M is the mutual between loops and R is the resistance of a loop. G z is a function of the dimensionless location of the loops and is the normalized radial field produced by the currents induced by an instantaneous plasma motion a t t

Contours of constant Gz are shown in Fig. 2. A loop with coordinstes ( a , d) may be placed on the figure once the plasma radius has been specified. The vaue of Gz

the loop is used in (1) t o obtain the radial field strength produced by the induced currents.

R a d l a l C o i l L o c a t i o n (a/r,)

Fig. 2 - Contours of Constant Effectiveness for Radial Field Produced by Two Loops.

Fig. 3 - Normalized Time Constant for Passive Loops.

These contour diagrams may be used with an "overlay" of a proposed machine design t o locate passive elements a t the optimum points (subject to other system constraints). An estimation can be made on the basis of the values of G z and B, t o determine whether or not the interaction of the plasma with the passive elements will be of sufficient strength. An example of this techinque will be given in a later section.

The time constant r0 in (1) can be shown to be given by:

= poua2G6, where

is the material conductivity. The function G6 is shown in Fig. 3 versus the loop location

and for different values of the ratio of cross-sectional radius t o loop radius r,/a. If saddle coils are used instead of loops, then the time constant ro should be scaled by the ratio of loop t o saddle resistance (i.e.

an adjustment for path length). The function G2 may still be used. This plot may be used to estimate the time frame over which active coils must be excited.

ACTIVE STABILIZATION

The positioning of control coils for active stabilzation can also use general contours of effectiveness [2]. The radial Geld produced by the loop pair (assumed to be series opposing) in terms of the energy stored in the coils, E,, can be written as:

where B,, is a function dependent on the nondimensional coordinates of the loop (a/ro, d/ro) and the cross-section to radius ratio r,/a.

Contours of constant B,, are shown in Fig. 4. If a coil location and plasma radius are given then the radial field produced for a given stored energy can be found. Similarly, if the desired radial field is known, the contours may be used t o determine the energy stored. Ratios of contour values may be used t o evaluate the energy storage requirements for coils a t different locations.

Radial Coil

Location

Fig. 4 - Contours of Constant Effectiveness for Radial Field Produced by Active Loops.

EXAMPLES

The nondimensional contours of constant effectiveness presented above are applied to a specific

tokamak geometry. The Toriodal Fusion Core Demonstration concept is chosen. A t this point,

a specific stability criterion must be selected. The required B,/Az is assumed to be a t least as

large as the applied steady state value of 6'B,/aa since this is the source of the destabilizing

force. If I , = 7.5 MA,

= 3.75 m, B, applied

-0.5 ' I , and the field index q f = -1,then the

required B, for a 3 cm. displacement is 0.133 T/m. The required G z for this case is, therefore,

0.2 or greater, since loops located on contours with a smaller value will not produce a reaction of

sufficient magnitude.

Cl-180

DE

Fig. 5 shows the contours of constant G:, with some critical characteristics of the tokamak superposed. An effective passive element must lie inside the G2=0.2 contour. The shaded area represents those locations that meet or exceed this criterion. The passive loops must be located near the first wall. Locations near the TF coil boundary, for exanlple, are not sufficiently effective.

Fig. 6 shows the ma.chine overlayed on contours of constant B,, with three points A, B, and C labeled as pot,ential locations for the control coils. The values of B,, f& the three points are given

R a d i a l C o i l L o c a t i o n (o/r,,) R a d i a l C o i l L o c a t i o n ( a / r o )

Fig.

- TFCD Outline Superposed on Contours Fig. 6 - TFCD Outline Superposed on of Constant Effectiveness for Passive Elements. Contours of Constant Effectiveness

for Control Coils.

in Table 1. If it is assumed that a radial field of 4.0 X I O - ~ T is requires, then (2) may be used with the values of B,, to find the stored energy for each case: If it is further assumed t h a t a charge time of .l00 seconds is required, then the peak power is as given. The effect of alternate coil locations may be rapidly evaluated by using the ratio of contour values.

Table 1. Active coil characteristics the TFCD example.

CONCLUSIONS

Several dimensionless contours of constant effectiveness have been presented which allow initial estimates of effective locations for both active and passive elements for the control of vertical plasma motion. These contours may be used to estimate power and energy requirements for the active system and to find effective locations for the passive elements. The contours are independent of specific machine geometry.

REFERENCES

[l]

Thome R., Pillsbury R., Langton W., and Mann, W.,PFC/RR-83-14, Plasma Fusion Center, MIT,1983.

[2] Thome R.,Pillsbury R., and Mann W., PFC/RR-83-15, Plasma Fusion Center, MIT,1983.