Dandl, R. A.

Dory, R. A.

Eason, H. O.

Guest, G. E.

Haste, G. R.

Hedrick, C. L.

Ikegami, H.

Jaeger, E. F.

Lazar, N. H.

McAlees, D. G.

McNeill, D. H.

Nelson, D. B.

Owen, L. W.

UNT Digital Library

RESULTS FROM THE ELMO BUMPY^TORUSIN A THEORETICAL CONTEXTC. L. Hedrick, R. A. Dandl, R. A. Dory, H. 0. Eason, G. E. Guest,G. R. Haste, H. Ikegami, E. F. Jaeger, N. H. Lazar, D. G.McAlees, D. H. McNeill, D. B. Nelson, L. W. OwenOak Ridge National Laboratory, Oak Ridge, Tennessee USAAbstract: Theoretical and experimental results from the ELMO Bumpy Toruswill be discussed with particular emphasis on macroscopic stability andtransport.The ELMO Bumpy Torus (EBT) is a steady state device [1] composed of alinked set of twenty four 2-to-l mirrors, arranged to form a torus withplasma heated by microwave power. The plasma has two basic components; amirror confined, high beta, hot electron plasma, forming hollow annulibetween each pair of coils; and a moderate temperature toroidal plasmathat threads each of the electron annuli. Experiments carried out dur-ing the past year have demonstrated the validity of the basic EBT premise:that plasma currents produced by the high-beta hot-electron annuli canprovide macroscopically stable plasma confinement by creating averageminimum-B. EBT has also exhibited confinement of particles and energy for10's of milliseconds, high plasma purity, and no perceptible difficultieswith field errors or convective cells. This paper summarizes the princi-pal experimental and theoretical features of the EBT research program.StabilityThree distinct, reproducible modes of operation, the C-, T- andM-Modes are observed at successive lower ambient gas pressure. TheC-Mode has a relatively high level of density fluctuations whilethe T-Mode is quiet. Theory predicts that when the hot electron componentbeta is in excess of about 15%, the local gradient in magnetic intensityshould reverse and satisfy the relevant stability criteria. Experimentallythe transition between the C- and T-Modes occurs for beta on the ordero f 15%DISTRIBUTION OF THIS DOCUMENT UNLIMITS/9Ideal MHD and guiding center theory would predict that the macrosco-pic modes of most importantance are pressure driven ballooning modes. Thesetheories are not applicable to the annuli themselves, since UK, UJ* > fl.- Amore correct, but geometrically simplified Vlasov analysis shows that theannuli are stabilized when the poloidal drift frequency of the electronsexceeds the ion cyclotron frequency. If the annuli are considered to berigid an MHD variational stability analysis of the toroidal core plasmashows that ballooning modes can only occur if the beta of the toroidal coreexceeds a critical value comparable to the beta in the annuli. These re-sults confirm that the present values of beta for the toroidal core are notlimited by gross stability requirements.Transport and HeatingIn the EBT plasma, electrons are heated by microwave power at fre-quencies of 18 GHz and 10.6 GHz. The 18 GHz is resonant (electron cyclo-tron frequency) for constant B surfaces on each side of the mirror mid-planes, while the 10.6 GHz source can provide lower off-resonant heatingas well as profile heating. Ions are heated,by Coulomb collisions withhot electrons. In the T-Mode, typical values of the plasma parameters aren (toroidal) <v 1-5 x 1012/Cm3; T (toroidal) = 150 eV; T.(toroidal) * 75 eV;e e l11 3x > 30 msec; n (annulus) =s 2.5 x 10 /cm ; T (annulus) £= 250 keV; g =s 0.4.For a theoretical estimate of operating conditions in the quietT-Mode, a simple point model has been developed in which radial variationsare characterized by typical scale lengths. We assume a neoclassicallifetime for ions as derived by Kovrizhnikh [2} for the bumpy torus. Tomaintain charge neutrality, the loss rate of electrons must equal that forions, requiring an ambipolar electric field in the radial direction. Ifthe rate at which electrons transfer energy to ions is that of classicalCoulomb collisions, the electron and ion temperatures and particle life-times can be calculated as functions of charged particle density.12 -3The results for a density of 2 x 10 cm suggest ion and electrontemperatures of 60 and 150 eV and particle lifetimes of about 20 msec.For weak ambipolar electric fields, the calculated particle lifetimesexhibit a strong inverse dependence on ion temperature, characteristic ofthe collisional regime. Higher electric fields and higher poloidal driftfrequencies are required to attain the collisionless regime where con-finement time increases with ion temperature.While this model gives results which are consistent with typicalparameters in the T-Mode, more detailed knowledge is needed of electrondynamics, ambipolar fields, diffusion coefficients and microwave powerdeposition to permit an unambiguous comparison with experiment. To up-grade the theory accordingly, we have devised a strategy based on thefollowing circular relations:1. Equilibrium magnetic fields depend on the pressure profile.2. Guiding-center drift orbits depend on the equilibrium magneticfield and ambipolar electric fields.3. Transport rates, which together with1 sources and sinks determinethe profile, depend on the guiding center drift orbits.3D equilibrium codes have been developed and are being improved andoperated to gain insight into the effect of finite beta on guiding-centerdrift orbits. The effect of finite-beta and .electric fields on guiding-center drifts is significant. To determine the resulting effect ontransport phenomena and study the effects of microwave heating, a kineticmodel of transport has been formulated using a Fokker-Planck equation todetermine the radial dependence of the distribution function and ambipolarelectric field. This is being implemented. Ultimately the loop repre-sented by 1), 2) and 3) above will be closed with transport and thepressure profiles then being determined self-consistently.The fluid-model computer codes developed in support of the tokamakprogram at Oak Ridge will have relevance to EBT, especially for questionsof neutral and impurity effects. The EBT experiments have demonstratedthe importance of the reflux of gas from the cavity wall in determiningthe source of particles required to maintain the plasma. The dominantsource of fresh ion-electron pairs is energetic neutral hydrogen, recircu-lated at the wall. Experiments provide estimates of the principal impuri-ties; these suggest that impurity ions drift to a wall (and are collectedthere) faster than they can diffuse inward, thus providing the observedhigh purity of the EBT toroidal plasma.A central research objective unifies all the experimental and theo-retical work on EBT reported here: to gain a working understanding of anymechanisms responsible for the loss of particles and energy from thesystem. Given the encouraging confirmation of the arguments advanced inproposing the EBT experiment, [3] we contemplate a sequence of devices toconfirm the present scaling. The next step calls for a moderate increasein magnetic field to perform scaling experiments using the existing torus.The second step would involve a large increase in the magnetic field and anew torus. These steps require development (already underway) of appro-priate high frequency microwave power sources.ReferencesResearch sponsored by the U. S. Energy Research and Development Admin-istration under contract with Union Carbide Corporation.[1] R. A. Dandl, e^ al, "The ELMO Bumpy Torus Program", ORNL-TM-4941(June 1975) and references cited therein.[2] L. M. Kovrizhnikh, Sov. Phys. - JETP 2£, 475 (1969).[3] R. A. Dandl, e£ al_, "The ELMO Bumpy Torus Experiment", ORNL-TM-3694(November 1971). - NOTICE -This report was prepared as an account of worksponsored by the United States Government. Neitherthe United States nor the United States EnergyResearch and Development Administration, nor any oftheir employees, nor any of their contractors,subcontractors, or their employees, nukes anywarranty, express or implied, or assumes any legalliability or responsibility for the accuracy, completenessor usefulness of any information, apparatus, product orprocess disclosed, or represents that its use would notinfringe privately owned rights.

Results from the ELMO Bumpy Torus in a theoretical context

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Results from the ELMO Bumpy Torus in a theoretical context

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