plasma ring heated by the electron cyclotron resonance using high power microwaves, and the greatly improved confinement of the PLASMA CONFINEMENT IN ECH BUMPY TORUS plasma particles by the ambipolar electric field. The contents of this review are,. (1) characteristics of the bumpy torus mag- M. FUJIWARA, T. KAMIMURA, H. IKEGAMI, NBT GROUP netic configuration and particle drift orbit, (2) plasma trans- port, (3) hot electron annulus and HHD stability, (4) electron Institute or Plasma Physics, cyclotron heating and ion cyclotron heating, and (5) present Nagoya Univt-sity, status and the future research program of the bumpy torus. Nagoya,Japan 2. NUMERICAL STUDIES ON PARTICLE CONFINEMENT IN BUMPY TORUS Bumpy torus is a magnetic confinement system consisted of ABSTRACT: Theoretical and experimental researches are reviewed toroidally connected mirrors, and is considered to be an S. = 0 on plasma confinement in ECH bumpy torus. Numerical study on stellarator with Et « e^, which has no rotational transform of particle confinement found that the particle confinement by magnetic field lines. Typically the magnetic mirror ratio EM " vacuum magnetic field .is the combination of toroidal and mirror- Bmax/Bo of each mirror section is roughly equal to 2, where Bm like trap depending strongly on spatial position. The ambipolar and Bo are the maximum and minimum magnetic field 1strength iosn10 the potential improves confinement greatly and the critical energy of toroidal axis, and the mechanical aspect ratio ci = Ro/rc > confined particles W is up to et'iefy) (here et and $ are the where Ro and rc are major radius and coil radius. inverse aspect ratio and plasma potential well or hill), while W -v e* in tandem mirror configuration. Some useful suggestions The orbit of a charged particle is closed in the poloidal are given to conventional neoclassical transport theory. Experi- plane by the poloidal drift due to the curvature of magnetic mental results are also surveyed, especially focused on the field lines and grad B. The poloidal precessional velocity scaling laws of the toroidal core plasma and hot electron ring depends strongly on the pitch angle of the particle velocity, parameters. The formation of hot electron rings is possible under and especially for v,,/v = 1 it is one order of magnitude, that is, some special conditions where ECH heating overcome the Coulomb by et times, smaller than that of a trapped particle. The orbit drag cooling by background plasmas. In other words this condition of the particle with v,,/v = I/I'SM does not close within the determines the maximum density of toroidal core plasma. Attain- toroidal vessel because the poloidal drift is cancelled out by able beta value or stored energy of hot electron rings is the positive (at the midplane) and negative curvatura (near the summarized by using experimental data of various machines. Brief mirror throat) of the mirror field lines. report is presented on recent experiments of ICH in NBT device. ICH not only contributes to ion heating, but affects the plasma Computed drift orbits in NBT device are shown in Fig.l for potential which has an important effect on transport. Some trapped particles with v,r/v » 0.3015, escaping particles v,,/v * results are also reported with respect to theoretical analysis of 1/i^H and toroidal passing particles v,,/v • 1. The circle of stability and equilibrium. triangular points shows the shadow of the coil casing, i.e., the mirror throat opening'to the midplane along the field line. From the figure, it is concluded that the mirror-trapped particles are well confined in each mirror sector, however, the particle passing through each mirror is rather poorly confined and the area, of the 1. INTRODUCTION closed orbit is narrow and localized in the area close to the inside wall of the torus. Theoretical and experimental research is reviewed on the plasma confinement by the ECH bumpy torus system which is consid- The spatial dependence of the loss cone in velocity space is ered to be one of the most promising candidates for the fusion shown in Fig.2. The region close to the inside wall of the torus reactor because of the following merits: (1) possible steady is characterized by both mirror and toroidal confinement of state operation, (ii) stable confinement of a high 3 plasma, particles with a narrow loss cone at v,,/v = 1/VEM and the confine- (iii) easy maintenance and good accessibility resulting from the ment of particles in the outside of the torus is similar to that simple structure of the magnetic coil systems. of an ordinary mirror machine which has the loss cone at v»/v < 1/vEjjï except that in case of the bumpy torus configuration, the The bumpy torus is a toroidal magentic trap consisting of a particle in the loss cone v,,/v < I/I'ÊM drift out to the walls set of linked magnetic mirrors. The main characteristic features approximately with the toroidal drift velocity and the loss rate of the ECH bumpy torus are thé HHD stable confinement by the decreases with increasing magnetic field, while in a mirror local magnetic well owing to the high 6, high energy hot electron device particles are rapidly lost in the transit time of L/v, 1S3 which is generally much smaller than the 90" Coulomb scattering plasma, the plasma potential may be 10 kV (* * Te) and it is time. possible to confine most of the fusion plasma particles whose energy W is less than several hundreds of keV. The particles The plasma potential has a strong effect on the confinement with W - 100 keV contribute mainly to the production of fusion characteristics because the E x B drift due to the ambipolar energy. Even alpha particles with the energy as high as 3.5 MeV potential is comparable to the magnetic drift (Er/B = <|>/Ba = could be well confined until they give up most of their energy to T/BRC) for particles with the thermal energy T. The effect of the core plasma. the potential on the particle confinement, that is, on the loss region, is shown in Fig.3 by changing the particle energy and 3. THE SURVEY OF THE EXPERIMENTAL RESULTS pitch angle for both cases of radially inward (N-type) and outward OF NBT-1, EBT-1, and EBT-S (P-type) electric field. The amazing feature is that the loss regions for the particles with 500-1000 eV are considerably The ordinary bumpy torus can confine charged particles as reduced in spite of the 40 V potential well in the N-type, and in is discussed in Section 1, but has been anticipated to be suscep- the P-type with 100 V of peak, potential. Probable reason is that tible to various MHD instabilities. In the past, various methods the critical boundary between confined and unconfined regime is were developed to overcome the difficulties and plasma stabiliza- determined by the condition of balance between toroidal drift and tion has been successfully achieved by the use of internal E x B drift, H/RCB = $/aB. From the result, it is concluded that poloidal rings which can produce rings of null magnetic field most of the plasma particles with the energy W < (R0/a)e

tokamak is localized in a narrow space around the drift axis of passing experiments for measurements of density, temperature, impurities, particles, and with the potential present the loss cone area is etc. with two notable additions — a heavy ion beam probe to filled with passing particles with so-called banana orbits (E- determine the local plasma potential (EBT/NBT) and a Li beam banana). (2) The maximum energy of the confined particle is given probe to determine the local electron density (NBT). by H = (e4>)(Ro/a) where $ is either potential depth for N-type or potential peak for P-type, as one can immediately notify, bumpy Electron-cyclotron-heating bumpy torus plasmas exhibit three torus with N-type potential configuration (EBT) is lossier than distinct operating modes (called C for cold, T for toroidal, and 1M that with P-type potential configuration (NBT). In fusion reactor M for mirror). The dependence of several plasma parameters on ambient neutral gas pressure is shown in Fig.5, which covers (3) Ions are heated by electrons through Coulomb interac- those three modes of operation for constant ECH power and mag- tion, but the temperature is relatively low. The ion energy netic field. The C-mode is characterized by a relatively high transport is dominated by charge exchange loss rather than thermal electron density but a low electron temperature and no appreci- conduction such as neoclessical transport, since the electron able hot electron ring. The T-mode is characterized by the density of the plasma is not high enough to prevent neutral hydro- existence of high-e hot electron rings, an electrostatic poten- gen atoms from the wall penetrating into the central part of a tial well, and improved confinement. The M-mode is characterized plasma. The parameter range is shown in Fig.6 it) which NBT, EBT by a very tenuous and unstable plasma with extremely high-B rings. and EBT-P plasmas are plotted for the ionization meanfree path Ai, Confinement results hereafter are presented only for the T-mode. the plasma radius ap and the electron density. Neutral-free plasmas can be expected in the next step devices such as EBT-P, The plasma parameters obtained by NBT/EBT machines are where the energy transport determined by plasma itself will be listed in Table 1. The scaling laws for plasma parameters are examined. studied vigorously by both groups and the present status is summarized as follows: ((4)) The plasmp a ppotentia l is observed as * Te. For NBT it is positivositive P-type, while in EBT it is observeobserved to be N-type. The (1) The density of toroidal core plasma increases with the didifferencf e may be ascribeid to thhe difdifferencf e in thhe wallll materialt . magentic field and the input powsr in the ordinary mode from the midplane of the outside wall (5) The behavior of the hot electron rings, which plays a I/o p crucial role to the macroscopic stability of bumpy torus plasmas, is studied in detail by NBT, EBT-1 and EBT-S device [7]. The scaling law for hot electron annul us parameters are observed The plasma density in T mode is determined in the following experimentally „ manner. Roughly speaking, the plasma density decreases with Th " B • nh - B » decreasing the ambient gas pressure pc in C mode regime and at some pressure and plasma density range the hot electron rings and consequently Bh is proportional to B as shown in Fig.7. The begin to build up by overcoming the barrier of the Coulomb drag energy balance for hot electron rings is determined by cooling described in later part of this section. The density of the toroidal core plasma in T mode is fixed just at this oper- Wi-nPpT,,. (1) ating point. The parametrical dependence of C-T transition is Here xn, ti and pu are the energy confinement time, the absorption a Pr_ r -r <^PT and n_ ,. T microwave fields. The most probable mechanism for energy loss is considered to be Coulomb- (2) The electron temperature varies linearly with the input drag in the currently existing devices NBT, EBT-1 and EBT-S. power [6], 1.0-1.5 As shown in Fig.8, recent NBT experiment on the measurement decay time of the X-band synchrotron emission, which is propor- The electron energy transport is compared with the neoclassical tional to hot electron energy density, reveals that the linear one including the favorable effects of ambipolar electric field, decrease of the decay time with background plasma density, which and experimentally it is verified that the energy confinement is well explained by Coulomb-drag processes. As is described in time with the assumption of the net input power is selfconsistent the scaling of toroidal plasmas, the maximum density of toroidal core will be determined by the condition under which the hot with the particle lifetime observed as the ratio of Ha line intensity to electron plasma density, that is, in the steady electron annul us can be formed without strong cooling. In this state plasma like bumpy torus plasmas, the particle confinement way, not only for MHD stability, the hot electrons and toroidal is essentially determined by the ionization time of neutral plasmas are strongly coupled with each other. The stored energy, particles within the plasma. But difficulty in the estimation of especially the density nn of the hot electron ring is observed to the net input power introduces ambiguity. increase linearly with py, but levels off at 4-5 kW input per ring. Several mechanisms are proposed such as the increase of 1S5 Coulomb drag because due to Increase In ne with /jv, reduction of One example of the calculation is shown in Fig.11, where the n by the increase of ne and nn> reduction of n due to increase in initial beta values of the bulk plasma and the hot electron ring Te or Tn, etc. are about 1 % and 25 % at the center, respectively. An equilib- rium state in this case is defined after the time step t = 10.24, (6) In the same way as in tokamaks with joule heating only, namely, approximately ten times the Alfvén transit time. Figure ions are heated by Coulomb collision with electrons which are 1 gives contour levels of the flux and indicates the local mini- heated by ECH of high power microwaves. Additional heating for mum B produced by the diamagnetic current of the hot electrons. ions must be necessary 1n future because of the decrease of the The magnetic gradients are increased in the vicinity of the hot energy exchange between electrons and ions in high temperature electron ring, while the curvature is hardly changed. plasmas. Since neutral beam heating causes the increase of the plasma density and spoils the merit of steady state operation, Some results on the stability criteria for flute and balloon- ion cyclotron heating 1s more favorable. In NBT device, ICH with ing modes are shown in Fig.12. The numerical equilibrium solu- the slow wave mode 1s extensively studied on the plasma density tions are obtained from the field Tine integration in the which 1s still to1o2 low 3to excite the fast wave mode effectively stability criteria. The results are shown in Fig.2; the condi- (ne = 0.5-1 x 10 cm" ) for m * 0, m • 1 modes. The excitation tion stable against flute and ballooning modes (O), stable for of RF waves In the slow wave mode is very sensitive to the loca- flute modes but unstable for ballooning modes (A), and unstable tion of an antenna and the waves is observed to propagate deeply against both flute and ballooning mode Ht). The condition given into the toroidal plasma and along the magnetic field line over by Van Dam and Lee [8] is also illustrated for comparison. The two or three cavities when the antenna 1s located near the mirror results presented here would be subject to further improvements throat. In this case loading resistance Increases and efficient for more realistic and improved models, numerical calculation, ion heating Is detected from the Doppler broadening of Ha lines as shown In Fig.9, when the excited frequency is tuned to the ion the geometry and profile effects such as the variations on the cyclotron frequency at the axis in the midplane. The wave is length and width of the hot electron ring, differnet pressure heavily damped at the magnetic beach. The other interesting profiles, etc. result Is the change of the ambipolar potential associated with In contrast to the rigid ring model, the present study show, ion heating, that Is, the P-type potential is enhanced and the that the position of the hot annulus at the equilibrium is effect on the plasma transport which is anticipated to be shifted inside or outside depending both on the pressure profiles improved, is now under study (Fig.10). and on the value of the ratio Sn/Bh. The shift may produce some compression of the bulk plasma, which could modify the equilibrium 3. ANALYSIS OF EQUILIBRIUM AND STABILITY IN A BUMPY TORUS and stability properties of the bumpy torus. The main role of the hot electron ring is to stabilize the toroidal core plasma magnttohydrodynamically. Actually the low The flute modes could be stabilized by the self-dug well of frequency fluctuation 1s observed to decrease drastically in T the ring over most of the ring region, however, a the outer edge, mode around the hot electron rings. In the present NBT and EBT, some line tying may be necessary if the plasma pressure extends . the beta value of the toroidal plasmas is still less than 1 % and beyond the edge of the magnetic well. the critical beta for stable confinement must be studied experi- mentally and theoretically from the viewpoint of the feasibility For the ballooning modes, stability criterion is more diffi- study on fusion reactors by ECH bumpy torus. Numerical analysis cult than that for flute modes because these modes distort and of equilibrium and stability 1s carried out on a bumpy cylinder. stretch the magnetic field lines, and the criterion involves only curvature which is not effectively modified by the finite Dynamical tensor pressure equilibria of a bumpy cylinder are beta. investigated numerically by using the two-dimensional magneto- hydrodynamic (MHD) equation. An Isotropic bulk plasma pressure For more realistic analysis on the stability of ECH bumpy and an anisotropic hot electron pressure are assumed, and the torus plasmas, geometry and profile effects such as variations in nonlinear evolution of two dimensional MHD equation are studied, the length and width of the hot electron ring and pressure pro- revealing that the hot electron rings play an important role in files should all be incorporated into the numerical calculations the equilibria of bumpy cylinder. Several stability criteria are of the equilibrium and the stability analysis. also studied on a class of MHD Instabilities from the numerical equilibrium solutions. The attainable beta value of the bulk 4. SUMMARY plasma for MHD equilibrium is estimated to be somewhat smaller ... than that predicted by the stability analysis of the rigid ring In closing this brief review on the bumpy torus concept, we IK model. present some remarks on undergoing experimental and theoretical researches: (1) Conventional neoclassical transport must be re- examined carefully in the meaning described in Section 1. (2) REFERENCES Experimental study is urged on the seal ing-law for the maximum density of toroidal plasmas, especially in relation to build up [1] DIMOV, G.I., ZAKAIDAKOV, V.V., KISHINEVSKII, M.E., Fizika and sustaining of hot electron ring. (3) Theoretical analysis of Plasma 2. (1976) 597; FOWLER, T.K., LOGAN, B.G., Comwnts stability is now in chaotic phase, so the experimental examina- on Plasma Physics and Controlled Fusion 2 (1977) 167. tion must be carried out against these theoretical results. The [2] Proc. of the EBT Transport Workshop, D0E/ET0112 (August, stabilizing effect of hot electron ring on the toroidal plasmas 1979). in T mode can be checked at least in existing devices NBT-1 and [3] MOHRI, A., HATSUDA, S., U0, K., Memoirs of Faculty of EBT-S. Engineering, Kyoto University, 32 (1970) 78; MOHRI, A., INDUE, H., Phys. Letters 35A (1971) 69; UCHIDA, T., et al., As shown in Table II, only two machines are operating in the in Plasma Physics and Controlled Nuclear Fusion Research world and the confinement studies have just started in the area (Proc. 4th Int. Conf. Madison) Vol.3, IAEA, Vienna (1971) of bumpy torus. High field devices are planned near future by 169; SYKOV, V.6., et al., Sov. Phys. Tech. Phys. 19 (1975) the use of superconducting magnets and high power millimeter-wave 1063. sources such as gyrotrons. The main subject of these devices is [4] DANOL, R.A., et al., in Plasma Physics and Controlled Nuclear to demonstrate the confinement of high density and high tempera- Fusion Research (Proc. 5th Int. Conf. Tokyo) Vol.2, IAEA, ture plasmas by the use of intense ion cyclotron heating and by Vienna (1975) 141. careful treatment against impurities employing material or mag- [5] FUJIWARA, M., et al., in Plasma Physics and Controlled netic limiter, etc. Nuclear Fusion Research (Proc. 8th Int. Conf. Brussels) CN-38/BB-4, IAEA, Vienna. [6] BIGHEL, L., COBBLE, J.A., Oak Ridge National Laboratory Report, ORNL-TM-7437 (1980). [7] UCKAN, N.A., et al., in Plasma Physics and Controlled Nuclear Fusion Research (Proc. 8th Int. Conf. Brussels) CN-38/BB-3-2, IAEA, Vienna. [8] VANOAM, J.W., LEE, Y.C., Proc. of the EBT Ring Physics Workshop (Oak Ridge, 1979).

197 TABLE I

EXPERIMENTAL VALUES NBT-SR NBT-FR EBT-1 EBT-S Mirror Ratio/Aspect Ratio 1.9:1/8:1 1.9:1/8:1 2:1/9:1

Bros (T) 0.3 0.18 0.65 1.0 4 4 4 Bulk Heating Power (W) 3 x 104 (8.5 GHz) 6 X 10 (8.5 GHz) 5 x 10 (18 GHz) 4.4 x 1Û (28 GHz) Profile Heating Power (W) 1 X 104(10.5 GHz) 1 x 104(10.5 GHz) 2 x 104(10.6GHz) 5 x 103 (18 GHz) 3 Power to Core Plasma (W) •y. 5 x 104 (4.5-6.2) x 10 (4.6-6).x 10 Average Core Plasma Radius (tu) 0.06-0.09 0.09 0.077 0.068 Major Radius R (m) 1.6 1.6 1.5 1.5

3 17 ,18 18 ,18 Central Density n in" ) 3-5 X 10 . 1 x 10 10 (1.2-2) x 10 Central Electron Temp. T(0) (eV) 50-140 12.5-20 250 •x. 500

Central Ion Temp. ^.(0) (eV) 80-90 •v- 100

Ion Tail Temp. Tt (eV) •v. 400 •\, 400

Potential Well Depth V (V) 50-70 •v. 190 •v. 250

3 16 ,16 16 ,16 Neutral Density nQ (m" ) (0.5-1) x 10 (0.5-1) X 10 (0.5-1) x 10 (0.5-1) X 10

CALCULATED VALUES 1 0.53-1.0 Dne Experiment («V ) 0.2-0.4 0.45-0.9

Dne Theory 0.1-0.43 0.7-1.4 0.9-1.4

4 (s) (2-4) x 10" (1-2) X 10 (1.2-2.8) x 10 (m3s) (0.6-2) X 1,104 (1-2) X 10 (1.4-5.6) x 10

181 ~i

Table II

IN OPERATION OPERATION IN 1982 PLANNING

NBT-1 EBT-1 EBT-S NBT-1H EBT-P (S.C.) NBT-2 (S.C.)

B T 0.3 0.64 1.0 2.1 2.5-3.5 res < > 1.0 R ( m) 1.6 1.5 1.5 1.4 4.S 3.5 fE 1.0 1.0 1.0 1.0 1.0 S 1.5 A 8.0 9.3 9.3 10.0 16 15 à (m) 0.1 0.1 0.1 0.1 0.18 0.2

N 24 co1l 2* 24 24 36 40 n (cm'3) MO12 I.SxlO12 4xlO12 4xlO12 1.7x1013 3x1013

Te (keV) 0.1-0.2 0.3 0.5 0.5 2 1-2 ^ (keV) 0.05+ 0.06 0.1 0.1 0.4 0.5 irO.I(ICH)

9 10 10 10 11 12 nt (s/cm ) MO 10 2x1O 2X10 SxiO MO f 8.5 GHz 18.0 28 28-35 60-110 60-110 nr|i1Tr[iiTTrrrrr"ï"" M Ji Vf\\\

y J ymjiff iP; H^K : ; ; : ; : (a) ; ;Stftîîii! lj =! = M m = = = : : : : i j j | i '{\ : : : : : : :::::: Mil ; i if i i [i M i M i M i i i 1- flflillllll Fig.2 The spatial dependence of loss cone in WT-1 without anbipolar potential. Vertical scale is pitch angle 6 • cos-Hv,,/y), and horizontal scale is radial position in the meridional plane of the torus. Particles in loss (b) cone are eliminated by hitting the coil throat. The region occupied with open circles is confined region and dotted part is loss region.

(c) Fig.l The drift surfaces of particles with various pitch angle (a) v,,/v - 0.3. (b) vn/v • 0.775 and (c) v,,/v = 1. The solid lines and broken lines in case, of (c) are calcu- lated by the longitudinal Invariant J» = 4v»d£ = const. The dotted star is computed by tracing the particles' 288 using the equation of guiding center motion. (b)

140 160 180 MAJOR RADIAL DIRECTION MAJOR RADIAL DIRECTION

Fig.3 The effect of ambipolar potential on spatial dependent loss cone 1s studied by changing the profile of the potential and the energy of particles, (a) corresponds to potential well (N-type, 2000 eV). 2fl °o.oo i.oo a.oo 3.00 11.00 1.00 2.00 3.00 1.00 °0.00 LOG 2.00 3.00 PfiRR ENERGT 1 KEV ) PfiRfl ENERGY ( KEV ) PflRfi ENERGY ( KEV )

LOSS HE010» ( P0rcNT[flL TTPE ( A PHRtICLE LOSS BEG10» ( POrENTtm. trPE I A . PBRriCLE LCSS P.EGJ0N I POTENTlML TTPE (A •

( xnn • isa.o l ( XHM - 152.O I xm - iss.o i

1.00 2.00 3.00 t.oa °O.00 ' 1.00 2.00 3.00 U. .00 1.00 3.00 3.00 •4.00 PRRfl ENERGY ( KEV ) PfiRfi ENERGY I KEV ) PRRfi ENERGY ( KEV )

PflflTICLE LOSS RECION ( POTENTISL TÏPE I A \PBBHCLE LOSS REGION 1 POTENTtfil TTPE pnnriCLE LOSS BEGION < POTENTIAL TTPE I/% . v i i

( XH« • 160.0 I t XMM ~ 1GH.0 1 t XHM - no. a )

Fig.4 The loss cone angle expressed in the parallel energy and perpendicular energy space in cases of (a) potential well 212 Fig.4(a) (N-type) and (b) potential hill (P-type). D 0

a:

"•-. '•. •••.•«

mm J.O C •-. "•• "*. "• °. '• • - ENERG l ^;v>. •,•••.•••.••-.•••••. O- o 0C o- Œ^ û_

g : '• •".•'••• O 0.00 1.00 2.00 3.00 4.00 °o!oo 1.00 2.00 3.00 4.00 °o.oa 1.00 2.00 3.no 1.00 PHRfl ENERGY 1 KEV ) PHRfl ENERGY [ KEV ) PRflf) ENERGY t KEV I pnnncLE L3SS REGION I POIEHUHL rrPE < g . LOSS RECtON < POTENIiDL r>PE I t PflflnCLE LOSS flEGICN I POrENIlflL TtPE ( S . ( XHB . 153.0 1 f xnn • ISfî.o i c xnn - iso.o i

i.bo a.ao n.oo °0.00 1.00 2.00 3.00 1.00 1.00 ' 2.00 3.Ô0 PRRA ENERGY I PHRR ENERGY I KEV ) PflRfl ENERGY ( KEV ) PBBTtClE LOSS REGION I POTENT IM. ftPE I 8 , : LOSS BEG;GN I PG;EM;:^L TTPE t 8 . (•nnricLE LOSS REGION I POTENTIAL TYPE ( 8 . v i i ( XHH • 1G0.0 I i xim • no.o i

213 25 I 1 1 1 1 1 1 1 P(18GHz) = 40 KW P (10.6 GHz) =0 M-MODE U T-MODE - -•—C-MODE-- W .^arbitrary units) -, 20 oREACTOR — 300 ,TOKAMAKS EBT-P>k\NBT-I ' 15 — 200

100 20keV 10 / 1 ! l\ d 10 12 14 16 18 20 P U fO"6.torr) lOkeV

fB =1.8 kA P,.,=4S kW n. (i/cc) 30 Fig,6 The plasma parameters in existing devices NBT-1, EBT-1, EBT-S and predicted parameters in planning machines are plotted in the diagram of ne, plasma radius ap and f-d ionization mean free path \\. / '20- C S !4 M S 3 _^<^\ . \ 10 2 • i Fig.S i (a) Line integral density and potential well depth as a %"v^— function of ambient neutral density in EBT-I. Also shown in the stored ring energy, W,. 10 20 (b) Line integral density, x-band synchrotron radiation, and dianagnetic loop signal as a function of ambient 214 l> i»10" * torn neutral density in NBT. 10 15 100 *p.. =6ûkW B. =2.2 kG V, A f / WITH RF M5W

WITHOU\ T \ RF 5 —. X 15eV

U/ce) OJ \ .] 50 100 150 Fig.7 The scaling of hot ring parameters. E.leV)

Fig.9 Ion temperature measured by the Doppler broadening of line with and without ion cyclotron heating.

300

200 200

10 15 40 60 ( x 10" cm" ) *P«(kW)

Fig.8 The dependence of the energy decay time of hot electron Fig.10 The increase of plasma potential associated with ion ring on the density of background toroidal plasmas. cyclotron heating. 2K i 15 flute Mod-B & Flux O i stable [ ballooning •A-: Stable flute —.1 Unstable ballo oning •A" Unstable [ fJ",\e m 10 ballooning • Van Dam—Lee to

% Fig.12 Results on stability criteria for flute and ballooning modes. Stable against flute and ballooning modes (O), • stable for flute mode but unstable for ballooning mode (A), and unstable against flute and ballooning modes Fig.11 Kod-B and levé] contours of flux are shown, which indi- (it). For comparison, the result by Van Dam and Lee is cate the local minimum in B created by the diamagnetic also plotted. current of the annulus. Bn ~ 25 % and Bp = 1 %,

L