Taylor-Couette Flow of Unmagnetized Plasma C. Collins,1, 2 M. Clark,1 C.M. Cooper,1, 2 K. Flanagan,1, 2 I.V. Khalzov,1, 2 M.D. Nornberg,1, 2 B. Seidlitz,1 J. Wallace,1 and C.B. Forest1, 2 1)Department of Physics, University of Wisconsin, Madison WI 53706, USA 2)Center for Magnetic Self Organization, University of Wisconsin, Madison WI 53706, USA (Dated: 26 October 2018) Differentially rotating flows of unmagnetized, highly conducting plasmas have been cre- ated in the Plasma Couette Experiment. Previously, hot-cathodes have been used to con- trol plasma rotation by a stirring technique [C. Collins et al., Phys. Rev. Lett. 108, 115001(2012)] on the outer cylindrical boundary|these plasmas were nearly rigid rotors, modified only by the presence of a neutral particle drag. Experiments have now been ex- tended to include stirring from an inner boundary, allowing for generalized circular Couette flow and opening a path for both hydrodynamic and magnetohydrodynamic experiments, as well as fundamental studies of plasma viscosity. Plasma is confined in a cylindrical, 11 −3 axisymmetric, multicusp magnetic field, with Te < 10 eV, Ti < 1 eV, and ne < 10 cm . Azimuthal flows (up to 12 km/s, M = V=cs ∼ 0:7) are driven by edge J × B torques in he- lium, neon, argon, and xenon plasmas, and the experiment has already achieved Rm ∼ 65 and P m ∼ 0:2−12. We present measurements of a self-consistent, rotation-induced, species- dependent radial electric field, which acts together with pressure gradient to provide the centripetal acceleration for the ions. The maximum flow speeds scale with the Alfv´encriti- cal ionization velocity, which occurs in partially ionized plasma. A hydrodynamic stability analysis in the context of the experimental geometry and achievable parameters is also explored. I. INTRODUCTION has been pursued as a model for understanding astrophysical systems, and theoretical investi- gations using both ideal magnetohydrodynam- Circular Couette flow (or Taylor-Couette ics (MHD) and extended MHD in plasma5 have flow, hereafter TCF) is one of the most fun- been examined. damental systems in fluid dynamics1{3 and was A TCF has recently been created using first investigated over 130 years ago. In TCF plasma, rather than liquids, in a laboratory geometry, a viscous liquid flows between two device named the Plasma Couette Experiment coaxial, differentially rotating cylinders. The (PCX) located at the University of Wisconsin- classic TCF profile is purely azimuthal, though Madison. The goal of PCX is to create a suffi- experiments in finite height cylinders often suf- ciently hot, steady-state, differentially rotating, fer from secondary, non-azimuthal Ekman cir- weakly magnetized plasma to study basic hy- culation due to end effects. While seemingly drodynamic and magnetic flow-driven instabil- simple, TCF exhibits a large number of distinct ities and dynamics specific to plasmas, such as flow states (which depend on the rotation rates two-fluid effects and neutral collisions. In PCX, of the inner and outer cylinders), making it toroidal plasma flow is controlled by electro- the ideal testbed for detailed experimental and static stirring assemblies at both the inner and arXiv:1403.2087v2 [physics.plasm-ph] 12 Apr 2014 theoretical studies of hydrodynamic instability outer boundaries. Flow profiles can be adjusted thresholds, nonlinear behavior, and transition so that the angular velocity decreases with ra- to turbulence4. Recently, TCF of a conduct- dius and the angular momentum increases with ing medium, such as liquid metal or plasma, radius, and thus mimic the Keplerian-like flows 2 of accretion disks (where Ω(r) = pGM=r3 ). A TCF of plasma operates in a regime dis- CENTER CORE tinct from either liquid or liquid metal TCF. ISOLATION CHAMBER Specifically, the degree of ionization introduces the possibility of momentum loss through colli- CENTER CORE sions with neutral atoms, and the resistive and STIRRING ASSEMBLY viscous dissipation varies with the plasma tem- TURBOMOLECULAR & perature Te and density ne. The relevant hydro- HELMHOLTZ COILS CRYO VACUUM PUMPS dynamic Reynolds number characterizing the ratio of the momentum advection by the flow to the momentum diffusion, Re = V L/ν, is gov- OUTER STIRRING ELECTRODES erned by the flow velocity V , the characteristic PROBE DRIVES size L, and Braginski viscosity; in an unmag- netized plasma, ν = 0:96v2 τ where v is the Ti i Ti SCANNING OPTICS TABLE ion thermal speed and τi is the ion-ion collision time. Also of interest is the magnetic Reynolds number, Rm = V L/η, which describes the de- gree to which magnetic fields are frozen into a moving plasma with magnetic diffusivity η. In FIG. 1. Major hardware components and cut-away terms of plasma parameters, view of the vacuum chamber. 4p −5=2 Re = 0:74 Vkm/sLmni,1011cm−3 Z µ Ti,eV (1) 3=2 −1 Rm = 0:84 Te;eV Vkm=sLmZ (2) The ratio of these quantities is the magnetic Prandtl number P m = Rm=Re = ν/η and is of order unity in PCX plasmas, a significant the plasma is achieved by extending the ro- advantage over liquid metal experiments where tation drive system to include all four cath- P m = 10−5 − 10−6. odes at the outer boundary. Plasma parame- If rotation is driven exclusively at the in- ters such as velocity, Te, ne, Vfloat are mea- ner boundary, TCF can become hydrodynam- sured with probe-based diagnostics, and a non- ically unstable above a certain critical thresh- perturbative method of line ratio spectroscopy old (set by the viscosity) and consequently ex- is also used to measure Te. A newly constructed hibits large-scale, secondary flows in the form center post assembly provides stirring on the of axisymmetric \Taylor" vortices, first studied inner boundary, resulting in a controlled, differ- in detail by G.I. Taylor in 19231. Exploring entially rotating flow which we use to explore the onset threshold for hydrodynamic instabil- the relevant dynamics of plasma TCF. Measure- ity is important in PCX, since Taylor vortices ments of a self-consistent, rotation-induced ra- govern the rate of momentum transport across dial electric field are also presented. Much ef- the sheared flow of plasma. Envisioning the use fort was made to maximize the induced flow, of this device for experiments concerning other and apparent velocity limits have been observed instabilities, such as the magnetorotational in- for various gas species (He ∼ 12 km/s, Ne ∼ 4 stability or generating a dynamo in TCF 6, re- km/s, Ar ∼ 3.2 km/s, Xe ∼ 1.4 km/s), that quires a thorough understanding of the impor- scale with a critical ionization velocity limit re- tant dynamical effects and thresholds for hydro- ported to occur in partially ionized plasmas. Fi- dynamic instability. nally, a hydrodynamic linear stability analysis This article reports on a number of recent ad- is performed to estimate the critical velocity for vancements to the experiment. Uniform, solid- the appearance of Taylor vortices at current ex- body rotation spanning the entire height of perimental geometry and parameters. 3 (a) (c) (b) 10 Swept Langmuir 9.5 OES 9 (d) 8.5 8 Te [eV] 7.5 7 6.5 6 0.15 0.2 0.25 0.3 0.35 (e) Radius [m] FIG. 3. Electron temperature vs. radius measured by the swept Langmuir probe and Optical Emis- sion Spectroscopy suggest uniform temperature in the bulk, unmagnetized region (0:1 < r < 0:3 m). Measurements were taken in a flowing argon plasma with 3 km/s solid body rotation (similar to Fig. 6e). FIG. 2. Newly installed center core assembly of Error bars are standard error of time-averaged mea- magnets and stirring electrodes. surements. II. DESCRIPTION OF EXPERIMENT These emission rings are absent at locations where center post electrodes are installed due In PCX, plasma is confined by a cylindrical to increased loss area. \bucket" assembly of permanent magnets, ar- Electron temperature is routinely measured ranged in rings of alternating polarity, to form with single-tip swept or triple-tip Langmuir an axisymmetric cusp magnetic field7. The field probes and has been confirmed using Optical is localized to the boundaries, leaving a large, Emission Spectroscopy (OES), a non-invasive unmagnetized plasma in the bulk, with aspect diagnostic which uses emission line ratios to de- < termine the electron temperature. The OES ratio Γ = height=(R2 − R1) ∼ 3. Plasma is produced with 2.45 GHz microwave heating to method9 has previously been developed by col- 10 11 −3 reach Te < 10 eV and ne = 10 -10 cm . laborators on an inductively coupled argon The waveguide launches mostly O-mode, im- plasma used in plasma processing with 1 < 10 plying a cutoff density limit at ne = 7:4 × 10 Te < 6 eV , but this is the first application to cm−3. Similar to other microwave powered mul- plasma with both higher electron temperature ticusp plasmas8, the PCX plasma is observed to (up to 15 eV) and ionization fraction (30%). have two distinct states. In the overdense state, The OES electron temperature measurements the plasma is produced by a surface wave dis- in PCX (Fig. 3) agree within 15% of Langmuir charge, exhibiting bright emission from the cen- probe measurements10. tral, field-free region of the plasma, and cusp The plasma is stirred using J × B forces in losses can clearly be seen. When the plasma the magnetized edge region, where current is is underdense, bright rings of emission are ob- driven by toroidally localized, electrostatically served, especially around the center core mag- biased hot cathodes. Viscosity couples the az- nets near the ECH resonant zone (Fig. 2e), indi- imuthal flow inward to the unmagnetized re- cating resonant electron heating and trapping.