Production And Study Of High-beta Plasma Confined By A .
Production and study of high-beta plasmaconfined by a superconducting dipole magnetD. T. Garnier, A. Hansen, M. E. Mauel, and E. OrtizDepartment of Applied Physics and Applied MathematicsColumbia University, New York, NY 10027A. Boxer, J. Ellsworth, I. Karim, J. Kesner, S. Mahar, and A. RoachPlasma Science and Fusion Center, MIT, Cambridge, MA 02139(Dated: October 28, 2005)The Levitated Dipole Experiment (LDX) [J. Kesner, et al. in Fusion Energy 1998 3, 1165 (1999)]is a new research facility that is exploring the confinement and stability of plasma created withinthe dipole field produced by a strong superconducting magnet. Unlike other configurations in whichstability depends on curvature and magnetic shear, magnetohydrodynamic stability of a dipolederives from plasma compressibility. Theoretically, the dipole magnetic geometry can stabilize acentrally-peaked plasma pressure that exceeds the local magnetic pressure (β 1), and the absenceof magnetic shear allows particle and energy confinement to decouple. In initial experiments, longpulse, quasi-steadystate microwave discharges lasting more than 10 seconds have been producedthat are consistent with equilibria having peak beta values of 20%. Detailed measurements havebeen made of discharge evolution, plasma dynamics and instability, and the roles of gas fueling,microwave power deposition profiles, and plasma boundary shape. In these initial experiments, thehigh-field superconducting floating coil was supported by three thin supports. The plasma is createdby multi-frequency electron cyclotron resonance heating at 2.45 and 6.4 GHz, and a population ofenergetic electrons, with mean energies above 50 keV, dominates the plasma pressure. Creation ofhigh-pressure, high-beta plasma is possible only when intense hot electron interchange instabilitiesare stabilized by sufficiently high background plasma density. A dramatic transition from a lowdensity, low-beta regime to a more quiescent, high-beta regime is observed when the plasma fuelingrate and confinement time become sufficiently large.PACS numbers: 52.55.-s, 52.50.SW, 52.35.-gI.INTRODUCTIONThe Levitated Dipole Experiment (LDX), shown inFig. 1, is a new research facility that was designed toinvestigate the confinement and stability of plasma ina dipole magnetic field configuration.1 The dipole confinement concept was motivated by spacecraft observations of planetary magnetospheres that show centrallypeaked plasma pressure profiles forming naturally whenthe solar wind drives plasma circulation and heating.2Unlike most other approaches to magnetic confinement inwhich stability requires average good curvature and magnetic shear, magnetohydrodynamic (MHD) stability in adipole derives from plasma compressibility.3–5 Plasma isstable to interchange and ballooning instabilities whenthe pressure gradient is sufficiently gentle even when thelocal plasma pressure exceeds the magnetic pressure or,equivalently, when β 2µ0 p/B 2 1.6 The ability ofthe dipole configuration to confine a high-beta plasmawithout magnetic shear may decouple particle and energy confinement, avoid the accumulation of fusion reaction products, and enable the dipole fusion power conceptto operate with a 3 He catalyzed D-D fuel cycle.7In this article we report the first experiments usingthe LDX device and describe the production of highbeta plasma confined by a dipole magnet using neutral gas fueling and electron cyclotron resonance heating(ECRH). The pressure results from a population of energetic trapped electrons that can be maintained for manyseconds of microwave heating provided sufficient neutralgas is supplied to the plasma.A number of previous experiments also used ECRHto produce high beta plasma.8,9,11,12 Energetic trappedelectrons were first generated in the ELMO experiments8where harmonic cyclotron absorption created a localized“ring” of weakly relativistic electrons (Eh 400 keV)within a plasma containing a larger density of cooler electrons. Linked magnetic mirrors, in which high beta electron rings were created, formed the bumpy torus device(EBT).9 In simple axisymmetric mirrors, internal magnetic probes were able to characterize the plasma equilibrium, and, during optimal conditions, multiple-frequencyECRH11 produced anisotropic plasmas that reached highvalues of local beta, β 40%, and high ratios of the perpendicular and parallel pressures, β /β 4.3. A similar study using a non-axisymmetric, minimum-B, magnetic mirror12 also achieved β 35% with weakly relativistic electrons having anisotropic pressure β /β 1.Early heating experiments, like those in EBT, weredone in “long-thin” unstable mirrors in which stabilizing plasma compressibility effects were insignificant. Thestability of the background plasma in EBT was believedto depend on a diamagnetic well created by the hot electron ring, and stability of the hot electron ring dependedon having a critical background plasma density. This
2symbiotic relationship resulted in a relatively restrictedstable operating regime (in terms of neutral gas pressure). Additionally early ECRH experiments were donein open field line systems and “line tying” may haveplayed a role in determining stability10 . In LDX thebackground plasma is stabilized by an entirely differentmechanism: the energy required for the plasma to expand(known as plasma compressibility) in a system characterized by a large magnetic flux expansion.The observations of stable high beta electron plasmas confined by axisymmetric mirrors are noteworthybecause the pressure gradients exceeded the usual criteria for MHD stability. Stability was possible becauseinstabilities driven by fast electrons acquire a real frequency, ω mωdh , proportional to the product of theazimuthal mode number, m, and the magnetic drift frequency of the fast electrons. The real frequency inducesa stabilizing ion polarization current13,14 that imposes aninstability threshold inversely proportional to the ratio ofthe line-averaged fast electron and ion densities, n̄h /n̄i .The high-frequency hot electron interchange (HEI) instability14 has a mode number, m 7, and a real frequencyabove the ion cyclotron frequency, ω mωdh ωci .This mode was observed in bumpy tori, and it destroyedfast electron confinement when n̄h /n̄i 40%.15 The lowfrequency HEI instability, first described by Krall13 , waspredicted to occur whend ln n̄ehm2 ωdh n̄i . 1 d ln V24 ωci n̄eh(1)Hwhere V d /B is the differential volume of a magnetic flux tube and m is a total perpendicular wavenumber16 and the over bar represents the flux tube average. Examination of Eq. 1 indicates that the hot electron density gradient is limited most severely at low hotelectron energy (since ωdh Eeh ) and at high hot electron fraction (n̄eh /n̄i ). The low-frequency HEI was observed in low beta plasma, β 1%, containing energeticelectrons trapped in a supported dipole experiment.17,18In the low beta dipole experiment, the HEI appearedwith low azimuthal mode number, m 1, a broad radialmode structure, and a complex, time-evolving frequencyspectrum.18 Intense bursts of instability induced chaoticradial transport17 , and nonlinear frequency-sweeping wasevidence for the inward propagation of “phase-spaceholes”.19In the experiments reported here, the trapped electronbeta was also limited by the low-frequency HEI, but whenthe neutral gas was programmed so as to maintain thedeuterium gas pressure between about 1-3 10 6 Torr,the fast electron pressure increased by more than a factorof ten and the stable high beta plasma could be maintained for many seconds. The high beta plasma generated a large equilibrium toroidal current, Ip 3 kA, thatis analogous to the ring current generated by high betaplasma in the Earth’s magnetosphere.20 Measurementsof magnetic field of the plasma current and the locationof fast electrons using x-ray imaging constrain modelsLevitation CoilHoistShapingCoilsInductiveCharging2mFIG. 1: (Color online) Schematic of LDX experiment showing the dipole magnet suspended within the vacuum vessel.Loops and coils measure the equilibrium plasma current, andprobes measure fluctuating potentials. Injected microwavepower strongly heats electrons at the cyclotron resonance.for the anisotropic pressure profile and allow estimatesof the plasma stored energy, Wp 300 J, and peak beta,β 20%. We also find that the presence of instabilitycreates hysteresis in high-beta plasma behavior. Highneutral fueling is required to create a high beta plasma,but, once stabilized, lower neutral fueling is needed tomaintain the high beta state.The remainder of this article is organized into threesections. First, the LDX experiment is described including a general account of the creation of LDX microwavedischarges. Next, the equilibrium of the anisotropic fastelectron pressure is parameterized by reconstruction ofthe plasma diamagnetic current from an array of magnetic sensors. Finally, observations of the hot electroninterchange instability that occur at the transitions toand from high and low plasma beta are described together with measurements of the levels of neutral fuelingassociated with stabilization and instability.II.DESCRIPTION OF THE LDX EXPERIMENTAs shown in Fig. 1, LDX consists of an internal superconducting coil located within a 5 m dia. vacuum chamber. The coil’s dipole moment is M 0.34 Id A·m2 , andexperiments have been conducted with Id ranging from0.75 and 1.2 MA. A large bore superconducting coil, located below the main chamber, is used to inductivelycharge the dipole coil. The dipole is lifted for plasma experiments by a vacuum hoist. In this configuration three1.5 cm dia. support rods intersect the plasma causing
3heat and particles to be lost from the plasma. (In futureexperiments the coil will be magnetically levitated, eliminating losses to the support rods.) Two shaping coils,arranged in a Helmholtz configuration, are located at theouter diameter of the vacuum vessel and may be used toproduce a magnetic separatrix. The effect on stability ofshaping the outer plasma will be reported elsewhere.Plasma diagnostics include 26 magnetic sensors to detect the plasma equilibrium current, movable probes tomeasure electrostatic fluctuations and edge plasma parameters, internal magnetic probes to measure magneticfluctuations, x-ray and visible light imaging cameras, anda microwave interferometer to measure the line-averageddensity across an equatorial path through the plasma.The x-ray camera contains a medical x-ray image intensifier sensitive to energies greater than 45 keV and waspreviously used during tokamak heating experiments.21A standard video camera is used to observe the fast electrons during the afterglow as described in Ref. 12. Themagnetic sensors include 19 magnetic field coils and Halleffect probes and 7 magnetic flux loops attached to thevacuum vessel. Several Langmuir probes can be moveddistances up to 0.4 m throughout the edge of the plasma,and two of these probes have high-impedance tips andhigh-speed amplifiers used to measure the potential fluctuations of the hot electron interchange instability andother lower-frequency perturbations of the plasma.A.Typical Microwave DischargeFig. 2 shows diagnostic signals from a typical LDXhigh-beta discharge. 5 kW of total ECRH microwavepower was applied to the plasma with equal amountsfrom 2.45 GHz and 6.4 GHz sources. The deuterium pressure was adjusted with four preprogrammed gas puffs.After an initial period lasting 0.25 s, the light emittedfrom the plasma abruptly increases followed by a moregradual increase in the perturbed magnetic flux near theouter equator. Since this detector senses 0.78 mV·s/kAfor a current ring located at 1 m radius, Fig. 2 indicatesseveral kA of equilibrium plasma current. Measurementsusing a microwave interferometer show the light emission is roughly proportional to the plasma line-density.By viewing the dipole magnet from several directions, weknow x-rays result from plasma bremsstrahlung and fromfast electrons driven inward to the dipole magnet. Whenthe ECRH power is switched off, the plasma equilibriumcurrent slowly decays proportional to the collisional lossrate of the trapped electrons.B.Three Regimes of the LDX PlasmaThe time evolution of plasma discharges created inLDX show the plasma to exist within one of three plasmaregimes: the “low density” regime (0 t 0.25 s), the“high beta” regime (0.25 t 4 s), and the “afterglow” (t 4 s) that occurs after the ECRH power is switchedoff. These three characteristic regimes are indicated inFig. 2 with the letters, “LD”, “HB”, and “AG”.In the low density regime, the plasma is characterized by relatively small diamagnetism ( 0.1 mV·s) andline-density ( 2.3 1016 m 3 ). Fig. 2 shows evidenceof rapid radial transport. A significant x-ray signal isobserved on a NaI detector with a radial view that includes the floating coil, which indicates inward-movinghot electrons striking the surface of the dipole coil. Negatively biased Langmuir probes at the outer edge of theplasma measure intense bursts of outward-directed energetic electrons. High-speed recordings of the electrostaticpotential fluctuations (described in Sec. 4) show frequencies that resonate with the magnetic drifts of electronswith energies ranging from 20-60 keV. As observed previously in a supported dipole experiment,17–19 the HEIinstability appears as quasi-periodic bursts with frequencies that are 0.3ωdh and sweep to higher frequencies,ω 1.8ωdh , during the nonlinear saturation of the instability. Visible light images of “low density” dischargesshow the light emission is localized to the equatorial planeindicating a strong interaction between the plasma andthe limiter on the outside of the floating coil, and theformation of a “disk” of deeply-trapped hot electrons.When the instability bursts become intense, the videoimages show inward transport of energetic plasma causing removal of dust and material from the dipole coil andits supports as indicated in Fig.2b. X-ray images showa strong x-ray emission at the outer floating coil limiterfurther indicating an inward transport of hot electrons.We conclude from these observations that the low density regime is associated with a quasi-continuous presenceof hot electron interchange instability that causes rapidradial transport of energetic electrons.The high-beta regime occurs after an abrupt transition that occurs when the neutral gas pressure exceedsa critical level that ranges from 2.5-3.5 10 6 Torr. Thelevel of neutral gas pressure required for the transitionincreases with the level of microwave heating power andvaries when the outer shape of the plasma is modified.Typically the transition occurs rapidly, within 2 ms, andcoincides with the ionization of the background neutralsand a rapid buildup of plasma density to a value 7-10times larger than during the low-density regime. A 1020 fold buildup of plasma diamagnetism occurs over amuch longer interval, 0.5 s. Initially, as the densityrises, the detected x-ray intensity decreases by an orderof magnitude consistent with the elimination of inwardhot electron flux to the floating coil. The sign of thecurrent collected by the negatively-biased edge probesreverses, so that positive ion saturation current is collected, indicating a sharp decrease in radial transport offast electrons. As will be described in Sec. 4, high-speedfloating potential probe measurements show the HEI instability is stable after the transition to the high-betaregime.Although the high-beta regime is grossly stable when
4LD4S50318005Gas Puff20.6AGVacuum (E-6 Torr)31HB5 kW ECRHPhotoDet (A.U.)0.40.20.0Edge Isat (A.U.)1.00.50.0-0.5-1.02.0Outer Flux (mV s)1.51.00.50.06420X-Ray (A.U.)02time (s)46FIG. 2: Example high beta plasma discharge created with 5 kW ECRH power and four gas puffs. (Left) Measurements show(i) the deuterium gas pressure within the chamber, (ii) the visible light from the plasma, (iii) the measured current from anegatively-biased Langmuir probe at the plasma edge, (iv) the magnetic flux near the outer equator, and (v) the x-ray intensity.(Right) Visible light frames from the low density, high beta and afterglow plasmas.compared to the low-density regime, infrequent and relatively short bursts of HEI fluctuations occur at a ratedetermined by the levels of neutral fueling and microwavepower. In Fig. 2, these small bursts are seen on the x-rayintensity signal and are sometimes accompanied by smalldrops in stored energy. This indicates that the high-betaplasma remains close to marginal stability. Video imagesshow “high-beta” plasmas do not cause particles to be removed from the dipole coil surfaces, but instead shows anincreased glow of the three coil support rods indicatingthe power deposition to the support rods increases duringthe high-beta regime. During the high beta regime, magnetic and electrostatic fluctuations appear that are easilydistinguished from the HEI instability since the observedfrequencies are below 5 kHz and are not associated withstrong radial transport.When the microwave power is switched off, the plasmaevolves to the regime called the “afterglow”. The plasmadensity decays within 10-15 ms, while the energetictrapped electron population decays much more slowly (120 s) consistent with the pitch angle scattering rate of hotelectrons. The slow decay of the diamagnetism indicatesthat the bulk of the stored energy is contained in the hotelectron population while the fast decay of plasma density indicates that a significant fraction of the injectedmicrowave power is required to maintain the density ofthe cooler plasma. During the afterglow, video images ofthe plasma show a crescent shaped light emission indicating a broadening of the hot electron pitch angle distribution as compared to the low density and high-betadischarge regimes. The behavior of the afterglow plasmaalso depends upon the level neutral pressure. If the neutral pressure during the afterglow decreases, very intensebursts of HEI instability appear that cause can lead tothe complete destruction of fast electron confinement andloss of trapped energy.III.CHARACTERIZING THE HIGH BETAPLASMAThe high beta hot-electron plasma component forms aring that is localized close to the field minimum (i.e. onthe outer midplane) at the ECH resonance location. Thediamagnetic currents that determine plasma equilibriumalso peak on the outer midplane and change sign on either side of the pressure peak. Estimates of the plasmapressure are made by computing the least-squares bestfit of a model to the magnetic diagnostics. We use ananisotropic pressure profile, with P P , that is similar to that used to study plasma equilibrium and stabilityin the magnetic field of a point dipole24,25 and given by
Fast Electrons: Anisotropic at ECRH ResonanceVisibleX-RayE 40 keV5507010110.62.45 GHzPressureContours0.40.20.0-0.26.4 GHzCurrentContours-0.4-0.6FIG. 3: (Color online) Superposition of the measured x-rayintensity and the visible light for single-frequency, 2.45 GHz,ECRH. The x-ray image shows localization of fast-electrons.4g30.40.60.81.0Radius (m)1.21.450701011, 50701012P!/P 531P (ψ, B) P̂ (ψ)(B0 (ψ)/B)2p where B φ ψ/2π2and B0 (ψ) is the minimum field strength on a field-line.With this model, the ratio of perpendicular to paral0.65 0.70 0.75 0.80 0.85lel pressure is a constant, P /P 1 2p. To fitRpeak (m) 2.45 GHzthis model to the magnetic measurements, the plasma6.4 GHzcurrent, Jφ (r, z) is related to the pressure through theself-consistent equilibrium, ψ(r, z). However, since theFIG. 4: Magneticreconstructionplasma pressure ofandplasmacurrent pressureprofiles for andECRHwith 2.45 GHFIG. 4:Magnetic ofreconstructioncurdipole moment of Jφ is less than 2% of the coil’s best-fit”anisotropicprofile,p /p" netic moment, the differen
beta plasma confined by a dipole magnet using neu-tral gas fueling and electron cyclotron resonance heating (ECRH). The pressure results from a population of ener-getic trapped electrons that can be maintained for many seconds of microwave heating provided sufficient neutral gas is supplied
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