Introduction to the Plasma Dynamo Experiment

Transcription

1 Introduction to the Plasma Dynamo Experiment Cary Forest CMO Fall Meeting Madison, Wisconsin 9 th OCTOBER 2009

2 Outline! motivation for flow driven experiments liquid metal experiments and results the plasma dynamo concept a prototype experiment in Couette geometry

3 Dimensionless umbers in this talk Cowling C B 2 2µ ρu 2 Magnetic Reynolds Rm µ 0 σul Reynolds Re U L ν Magnetic Prandtl P m µ 0 σν

4 Minimum requirements for experimentally addressing each Plasma Process in Astrophysics λ Plasma Process Rm crit Re C L β large scale dynamo laminar 100 < 100 Cowling with turbulence 500 > small scale dynamo ?? MHD turbulence Re MRI with mean field 10 1?? without mean field ?? B field stretching 100 < Plasma Instabilities Re Large, High Te, fast flowing plasmas Low B, fast flowing d to the condu plasmas Long pulse lengths: tpulse>>τ σ = µ 0 σa 2 C B 2 2µ ρu 2 Magnetic Reynolds Rm µ 0 σul Reynolds Re U L Magnetic Prandtl P m µ 0 σν ν

5 Flow driven instabilities convert mechanical energy to magnetic field dynamos 1. Begin with small magnetic field ( V/V Alfvén ) 2 >>1 ) 2. tir until Rm=μ 0 σvl > Rm crit 3. Magnetic field spontaneously created Plasmas are difficult to confine liquid metal experiments (Pm=Rm/Re<<1, Rm MAX ~ 150) on dynamos and MRI

6 The Madison Dynamo Experiment (Rm<150, Re ~ 10 7 )

7 Liquid Metal Experiments are limited: the next frontier for flow driven instability studies should be plasma based Liquid metals have advantage that confinement is free and conductivity is independent of confinement, BUT: Unfortunate Power caling Limitation: P mech ~ Rm 3 / L Prandtl umber is always very small : Rm << Re Plasmas have the potential for Variable Pm (= Rm/Re) Rm >> 100 intrinsically include plasma effects important for astrophysics (compressibility, collisionality) broader class of available diagnostics

8 Plasma Dynamo Facility is feasible to study high Rm, high V/V Alfvén plasmas Axisymmetric Ring Cusp edge confinement provided by 1.5 T, dfeb Magnets high power plasma source using LaB kw, DC power supplies similar to LAPD, CDX technology Challenges cooling of magnets insulators axisymmetric rings of permenent magnets LaB Cathode m >200 kw - +

9 Multipole Magnetic Field can be used to drive flow at edge B E Arbitrary Vφ (r = a, θ) V - +

10 Plasma Parameters plasma radius a 1.5 m density n m 3 electron temperature T e 2 20 ev ion temperature T i ev peak flow speed U max 0 20 km/s ion species H, He, e, Ar 1, 4, 20, 40 amu magnetic field r < 1.2 m <0.1 gauss magnetic field at cusp >10 4 gauss current diffusion time µ 0 σa 2 50 msec pulse length τ pulse 5 sec heating power P < 0.5 MW Rm max > 1000 Re P m C 10 4 β 10 4

11 Formulary of Key Dimensionless Parameters Magnetic Reynolds umber Rm µ 0 σul 1.5 Reynolds umber Re U L ν 8 Magnetic Prandtl umber P m µ 0 σν 0.18 B 2 2µ Cowling umber C ρu Lundquist umber Lu Rm C 1/ Magnetization Ion Collisionality Plasma Pressure β λ mfp ρ e L L µ 0 nt 40 B 2 T 3/2 e,ev U km/sl m Z a m U km/s µ 2 n 18 T 5/2 i,ev T 3/2 e,ev T 5/2 i,ev µ 2 n 18 B 2 G µn 18 Ukm/s 2 T 3/2 e,ev B GL m Z µn 18 T 1/2 e,ev B G L m T 2 i,ev n 18 L m n 18 T e,ev BG 2

12 Von Karman flow: IMROD imulations using E tan =R Ω B r to control boundary rotation with cusp field

13 Toroidal where σ is the conductivity of the fluid, v0 a characteristic speed, and a the radius of the sphere, and P m, the magnetic Prandtl number, which describes the ratio of viscous to magnetic diffusion. o-slip boundary conditions are used, and an electrically-insulating outer boundary is assumed. By varying the outer toroidal velocity field boundary condition different flow regimes have been studied. In ection II we present boundary conditions which result in flows which display dynamo action. In ection III we describe2how Keplerian flow profiles have also been simulated. These simulations are unstable to the Magnetorotational Instability (MRI) when exposed to an axial applied magnetic field. Two Vortex Plasma Dynamo Flow can be driven at boundary (spherical Von Karman Flow) using incompressible DYAMO code Toroidal peed [arb] II. Energy [arb] V Angle [Radians] FIG. 1: Toroidal boundary condition which generates a Von Ka rma n-type flow. V! Vpol DYAMO IMULATIO Liquid metal experiments have recently succeeded in 0.0 magnetically self-exciting. The first two of these cases2,3 used pipes and baffles to carefully prescribe the flow. The systems were not simply connected and the role of turbulence in the experiments was unclear. The latest ex-0.5 periment to dynamo is based on the Von Ka rma n flow13. It is simply connected, impeller driven, and is very turbulent. o experiments based on the Couette flow have -1.0 magnetically self-excited That a flow generated by a differentially rotating outer Angle [Radians] boundary might magnetically self-excite is a bit of a surprise. It is difficult to generate the poloidal flow needed # 10-2 Velocity to sustain dynamo action14a. Von This difficulty manifests itfig. 1: Toroidal boundary condition which generates Magnetic self in the very large critical magnetic Reynolds numbers, Ka rma n-type flow Rmcrit, required for these flows to self-excite. V 10! -0.5 A. Ka rma n Flows VVon pol 3 t = 2.62"# Vpol 0.0 V [arb] Plasma Rm=300, Re=100 Te=10 ev U=10 km/s, n=1018 m-3 Rm = 375, which explains the very slow growth rate of field. Hydrogen the magnetic As is required for axisymmetric velocfig. 2: teady-state velocity field generated by the toroidal boundary condition given in Figure 1, before the growing magnetic field becomes important. In the left hemisphere are of toroidal speed, and in the right hemisphere the contours are the contours of the poloidal stream function. ote that, as indicated in Figure 1, the peak speed is 1, but the scale range has been reduced for clarity. The first category of flows which magnetically selfexcite is based on the Von Ka rma n flow. In this case 10 the outer boundary rotates in opposite directions near the poles of the sphere and rotates relatively little near the 10 equator. The 15 boundary condition is presented in 5 crit TimeFigure [!"] 1, and is constructed by having non-zero boundary conditions for the even-numbered spherical harmonic ity fields, the excited magnetic field is non-axisymmetric, components, " = 2, 4, 6,Plasma 8. The Dynamo steady state velocity pence, Reuter and Forest, A pherical Experiment, dominated by m = 1 modes. field which results from this boundary condition, for FIG. 3: Energy versus time for the boundary condition given 700, 470 Rm = 400 andp.p m = (2009). 1, is given in Figure 2. The vein Figure 1.The ForAstrophysical this run Rm =Journal 400. locity field is counter-rotating in the toroidal direction, -10

14 mall cale Dynamo at Pm>1 Rm=1000 Re=400 Plasma Te = 13 ev Ti = 1 ev deuterium U = 15 km/s n = m -3

15 Prototype Experiment is being constructed to study a plasma Couette Flow

16 Different flows in cylinder Rigid rotation (rotating convection) Von Karman flow (two vortex dynamo)

17 Plasma Couette Flow Experiment is a prototype for dynamo experiment and will be used to study MRI

18 MRI dispersion in Plasma Couette Flow

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21 CMO Workshop on Flow Driven Instabilities and Turbulence in high beta plasmas and Kick-off meeting for the Madison Plasma Dynamo Experiment Organizers: Cary Forest, Hantao Ji, Ellen Zweibel, Ben Brown, Fausto Cattaneo, teve Cowley Dec 15-17, 2009 University of Wisconsin, Madison The purpose of this CMO sponsored workshop is to (1) review the theoretical understanding of plasma processes beyond incompressible MHD on flow driven instabilities such as the dynamo and magnetorotational instability in astrophysical plasmas, and (2) to consider possible experimental scenarios where these processes might be investigated in plasmas. The format will pairs of coordinated talks beginning with the reviews of the process and astrophysical significance, and followed by a briefer discussion of how such processes might be studied in new experimental configurations (including, but not limited to the Plasma Dynamo Experiment under construction at the UW). The third morning will be a design review for the new experiment. An ulterior motivation for this meeting is to assess experimental opportunities in experimental plasma astrophysics in preparation for the upcoming Plasma Astrophysics meeting, to identify any low hanging fruit for plasma based experiments, and to assure that the appropriate diagnostics are being planned for. peakers Process Astrophysicist/Theorist Experimental/Modeling cenario Issues Charge: Review of the physical process and where topic is important in Astrophysics. What parameter regimes are necessary to learn something important? What needs to be measured? Charge: Conceptual design of plasma experiment (in PDX or otherwise) and feasibility. Hardware implementation, geometry, and required plasma parameters. What can be measured? MHD Dynamos tas Boldyrev (confirmed) Cary Forest (confirmed) From a pure MHD standpoint, how do we optimize the experiment for studying outstanding questions in dynamos? What flow topologies are optimal? Can time dependent (Galloway Proctor flows) be devised in a sphere? How does compressibility and/or high Pm possible in plasma change outlook. Plasma Dynamos teve Cowley (probably) Where and when do two fluid or kinetic effects become important in astrophysical dynamos? What parameter regime and geometry is optimal for studying this in experiment? Hall effects; firehose, mirror

22 Plasma MRI Greg Hammet Hantao Ji (Tuesday only) tandard MRI flow; what will Hall (both MHD and neutral collisions) effects, anisotropic pressure and collisionless MRI look like. What do we need to diagnose it. Rotating Convection (compressibility and stratification) Juri Toomre Ben Brown kunk works on compositional/temperature/magnetic buoyancy driven instabilities in stratified, rotating plasmas; ECH applied to boundary provides heating and buoyancy; Role of Reynolds stress on rotation profile; stratification; Magnetic buoyancy Plasma Turbulence at high Beta Bill Dorland (confirmed) Troy Carter (confirmed) ee MRI and Plasma Dynamos; elf-excitation not critical; chaotic stirring is. Turbulence in near equipartition. Ion heating. Inertial range; transition from unmagnetized to magnetized (anisotropy) Jets Driven bykeplerian Disks Dmitri Uzdensky (John Everett) Ken Fowler/Gennady Fiksel Plasma Gun array injecting into high beta plasma; equilibrium, loss of equilibrium, collimation; focus on steady state aspects and role of external plasma pressure Pulsar Winds and hocks Flow driven reconnection Jonathan Arons (confirmed) Barrett Rogers Concept: rotating dipole built into source in center in center of sphere, spewing off magnetic fields of alternating polarity; as density drops off, Alfvén velocity approaches speed of light. Heliospheric, sectored structure of heliosphere solar wind. Anomalous Cosmic Rays from Fermi accelleration from reconnection(drake). 2D Reconnection of multipolar magnetic fields in spherical source, with fields that drop off outward. Rotating plasma wind tunnel impinging on a dipole. Disk Dynamo/tar disk collisions Partially Ionized MHD Ellen Zweibel