x - .2. v 7 .d>. oml 0RNL/TM-9520 Experimental Study of Equilibrium in a Bumpy Torus S. Hiroe J. A. Cobble R. J. Colchin G. L. Chen K. A. Connor J. R. Goyer L. Solensten 5; ',•-•• i ' i P DISTRIBUTION OF THIS DOCUMENT IS UNUIftTTEB ORNL/TM—9520 DE86 014415 Pist. cH^W^O f,g Fusion Energy Division Experimental Study of Equilibrium in a Bumpy Torus S. Hiroe J. A. Cobble R. J. Colchin G. L. Chen Fusion Energy Division K. A. Connor, J. R. Goyer, L. Solensten Rensselaer Polytechnic Institute Troy, New York Date of Issue: June 1986 Prepared by the OAK RIDGE NATIONAL I-ABORAI OKY Oak Ridge, Tennessee 37831 operated by <lkT_ MARTIN MARIETTA ENERGY SYSTEMS, INC. for the U. S. DEPARTMENT OF KNKRGY under Contract No. DE-AC05-840R21400 OlSTRlBUT,0«0FTHlSD0CU^T^^ CONTENTS ABSTRACT v I. INTRODUCTION 1 n. EXPERIMENTAL RESULTS 3 m. DISCUSSION 15 A. Formation of closed potential contours 15 B. Inward displacement of potential contours 22 C. Electrostatic beta limit 26 D. Force balance 28 E. Explanation of potential deformation 33 TV. CONCLUSION 37 ACKNOWLEDGMENTS 39 REFERENCES 41 iii ABSTRACT Plasma equilibrium in the ELMO Bumpy Torus (EBT)1 was studied experimentally by measurements of the electrostatic potential structure. Before an electron tail population is formed, the electric field is found, roughly speaking, to be in the vertical direction. The appearance of a high-energy electron tail signals the formation of a negative potential well, and the potential contours start to nest. The potential contours are shifted inward with respect to the center of the conducting wall. The electric field between the plasma and the conducting wall forces the plasma inward, balancing the outward expansion force. This force balance provides a horizontal electric field that cancels the concentric radial electric field locally at the separatrix of the potential contour and leads to convective energy loss. v I. INTRODUCTION There has been much interest in the kind of equilibrium that can exist in a closed magnetic-field-line system without a rotational transform. Although there has not yet been an experimental discussion of the equilibrium in an electron cyclotron heating (ECH) bumpy torus, there have been several theoretical discussions.-'3,4 Budker2 has pointed out that the E x B poloidal rotation due to the centripetal electric field is equivalent to the existence of a rotational transform with V(B/qR replaced by E, where vj is the velocity parallel to the toroidal magnetic field, q is the safety factor, and R is the major radius. The equipotential contours4 shift inward from the magnetic axis in the case of the potential well. Hereafter, we will only be concerned with the plasmas whose pressure profiles are hill-shaped and whose potential profiles are well-shaped (with exceptions as noted). Bulyginskii et al.5 qualitatively analyzed a mechanism for the formation of an equilibrium plasma configuration in a current-free toroidal plasma. Sufficiently strong centripetal electric fields for an equilibrium were produced by the charge separation caused by toroidal drift and/or the preferential loss of particles. They also carried out a qualitative analysis of the evolution of a plasma left to itself and tending toward equilibrium in the drift approximation. Closed drift trajectories are at least necessary for the potential contours to nest. Thus, when the potential contours evolve from a lack of equilibrium to closed equilibrium configuration, additional drifts are needed to cancel the outward E x B drift due to a lack of equilibrium. The inertial drift is one of these additional drifts. Bulyginskii et al. also pointed out the relation of the inward shift of the potential center to a conducting vacuum vessel and discussed the electrostatic force balance. 1 2 Popkov6 examined the equilibrium and stability of a charged plasma in a toroidal magnetic field and in an external electric field. He found that only a low-density plasma (ci- 1 <s 1) can have a stable equilibrium, where ti is a dielectric constant. On solving the Poisson equation, the equipotential surfaces were found to be concentric, nested tori whose major radii increase as the minor radii. Beyond a certain plasma parameter, the equipotentials cease to be closed where d$/dr = 0. The potential contour d<J)/dr = 0 is called the potential separatrix. Locating the separatrix of ne potential contour outside the torus led to an electrostatic beta limit of [3K = 2<p>/E- <R/a - 5/4, where <p> is the averaged plasma pressure and a is the plasma minor radius. Recently, El-Nadi7 analyzed the high-density plasma equilibrium (eL- ls> 1) in a bumpy torus (not a simple torus). The density was assumed to be an arbitrary function of <I> + Te /e In U = $ df/B rather than the potential <E> because of the bumpiness. He pointed out that the Poisson equation for the electrostatic equilibrium was equivalent to the Grad- Shafranov equation for the magnetic equilibrium. The general characteristics of the potential structure in the plasma are qualitatively similar to Popkov's results, except that El-Nadi did not discuss the external electric field and the stability of this equilibrium. Thus, many physicists have suggested electrostatic equilibria in closed magnetic field-line systems. The important points of these works are: 1. The plasma equilibrium may be attained with concentric, closed potential contours without a rotational transform (electrostatic equilibrium). 2. A horizontal external electric field is necessary to sustain the equilibrium. 3 3. The equilibrium potential contours are shifted inward with respect to the center of the boundary (metal wall, hot electron ring, etc.). 2 4. The electrostatic beta value of pE = 2<P>/EE is found to be limited when the potential separatrix forms in plasmas. Besides electrostatic equilibrium, the possible existence of an equilibrium without the electric field in the ELMO Bumpy Torus (EBT) was examined. FreidbergS calculated the analytical toroidal equilibria of the EBT configuration by means of an asymptotic expansion in the amplitude of the "bumpiness." Equilibria containing a magnetic well were found. It was shown that a toroidal plasma shifts inward to counteract the 1/R outward toroidal expansion force. The purpose of this paper is to study experimentally the equilibrium in a particular closed field-line device - the EBT. Experimental results are presented in Sec. II and are discussed in Sec. HI. Concluding remarks are given in Sec. IV. II. EXPERIMENTAL RESULTS A prolonged effort has been made by a group from the Rensselaer Polytechnic Institute (RPI) to obtain electrostatic potentials in EBT by means of a heavy-ion-beam probe.9 Recently this probe has been made capable of measuring two-dimensional equipotential (2-D<l>) contours, thus enabling us to discuss experimentally the electrostatic equilibrium in an ECH bumpy torus. The EBT1 consists of 24 simple mirrors that are connected toroidally. The major radius is 1.5 m, and the minor radius is ~0.1 m at the mirror throat. The mirror ratio at the magnetic axis is 1.9. Vacuum mod-B contours and magnetic field lines are plotted in Fig. 1. The fundamental and second ORNL-DWG 84-3737 FED MOVABLE LIMITER ALUMINUM WALL> CsCHARGE THOMSON EXCHANGE /SCATTERING SPECTROMETRY 5ch DIAGNOSTIC HARD NEUTRAL X-RAY BEAM MACHINE FUNDAMENTAL RESONANCE SOFT CENTER X-RAY GAS FEED LIMITER RGA BEAM OPTICAL VIEWPORT INTERFEROMETER (4 mm) Fig. 1. Location of diagnostics used for this experiment are schematically indicated in the left half of the figure. In the right half, the fundamental electron cyclotron resonance surface, the second cyclotron resonance surface, and the. magnetic field lines are plotted. Position X = 0 corresponds to the machine center, "a" to the center of the bumpy field, "b" to the "operational position" of the movable limiter, and "c" to the position 1.5 cm inward from the field line intersecting the second cyclotron resonance. 5 electron cyclotron resonance positions in this plot correspond to normal EBT-S operation. The magnetic field strength at the fundamental resonance is 1 T. The maximum magnetic field (B()) in the midplane is 0.725 T, and the maximum magnetic field point (magnetic axis, center of the bumpy field) is located toward the inside of the torus. The inward displacement of this point from the machine center is about 3 cm in the midplane. The center of the mod-|B| contours for the second electron cyclotron resonance in the midplane (ring center) is displaced inward by Ar = 1.5 cm from the machine center (geometrical center of a cavity). To study the boundary conditions experimentally, a movable limiter was installed in one of the 24 cavities. The positions denoted by b and c in Fig. 1 are called the operational position and the inside position, respectively. The heavy-ion-beam probe cavity is located three cavities away from the limiter cavity. A Thomson scattering system was employed to measure the bulk electron density and temperature. It was located 11 cavities away from the limiter cavity. The EBT plasma is produced by high-power microwaves (P^). The frequencies of the microwaves (fM) are 18 and 28 GHz. The device is called EBT-1 when f„ = 18 GHz (B0 = 0.5 T); it is called EBT-S when fM = 28 GHz (B0 = 0.725 T). Typical operation was carried out by keeping constant and changing ambient pressure (p0). When the machine was operated in this manner, there were three different operational modes,1 called the C-mode (high p0), the T-mode, and the M-mode (low p()). The transitions between the individual modes are called the T-C transition and the T-M transition. Stability at the T-M transition has already been discussed.10 The hot electron instability prevents operation at lower pressure.