Catalin Teodorescu, William Young, Richard Ellis, Adil Hassam Experimental evidence of MHD plasma centrifugal confinement in a shaped “open” magnetic field configuration Catalin Teodorescu, William Young, Richard Ellis, Adil Hassam

Maryland Centrifugal Experiment Plasma breakdown in EB configuration Applied voltage:  20 kV (5 MJ max.) Mirror ratio: Rm ~ 9 (Bmid  0.23 T) Hydrogen or helium, puffed or static fill: p0  10 mTorr Pulsed experiment: t  10 ms Cp=Cvac plasma capacitor Rp plasma “leakage” resistance

MCX schematics and plasma parameters V insulator uExB=E/B Stainless steel core (HV electrode) LGFS Expected E(r) Plasma terminates axially on insulators  magnetic field lines are equipotential lines. Central core and vessel are “limiters” (set LGFS). Innermost LGFS is at HV potential; outermost LGFS is at zero potential. Plasma length: Lp = 2 m; plasma cross-section: a = 0.2 m ~ 102 i at midplane. Electric field peaks in the plasma center, vanishes outside LGFS.

MCX diagnostics HV feed-through Voltage divider (core - ground) Rogowski coil (on core) 3-D and 1-D magnetic probes External diamagnetic loops Multi-chord spectrometer IR and visible interferometers H detectors HV feed-through r z LGFS 5-chord visible spectrometer 2 Mach-Zehnder heterodyne interferometers with IR lasers placed at midplane and off-midplane

MCX plasma parameters are quasi-steady for 1000’s of MHD instability times, much longer than in non-rotating magnetic mirrors MHD m MHD instability growth time MHD ~ 2 - 20s Measured momentum confinement time m ~ 500s No “major disruptions”  MHD Stable?

Plasma density measurement yields a chord-averaged value Location of interferometer laser beams through plasma: Midplane: z2=0; r2=15 cm Off-midplane: z1=85 cm; r1=6 cm 2 1 2 1 r l

Plasma density and diamagnetic flux are large at the magnetic minimum DML2 DML1 2 1  n2/ n1=12 DML2 DML1 2 1  n2/ n1=0.4

Density changes both at midplane and off-midplane with Rm Values at t=2 ms averaged over one momentum confinement time (=100 s). Fixed applied parameters except for Rm=B(z=130)/B(z=0).

Density ratio and diamagnetic flux ratio scale exponentially with magnetic mirror ratio  r1DML r1 Mirror Ratio: 2 r2 r1DML r1 Average values over 100 s (one momentum confinement time) at t=2 ms in the discharge.

Spectroscopic measurements of plasma rotation and ion temperature profiles yield information on sonic Mach number Line observed: C2+ of 4647.42 Å Measured at t=2 ms in the discharge. Off-midplane Ti is comparable to Ti at midplane.

2D solution of Grad-Shafranov equation with plasma rotation is calculated 2D code solves Grad-Shafranov with rotation: (u2/r)||= ||p assuming Ti()=constant and Te=0. n1(r1,z1)=n2(r2,0)exp{-Ms2/2[1-(r1/r2)2]}  Young et al.,mss, 2009 Input: profiles for Ms and density at midplane (from n2, u and Ti measured values). Output: profile of n1(r1, z1).

Theory fits the trend of measured data Measured Ms profiles available only for Rm=8. Chord-averaged measurements of Ms were made for Rm<8. Average of a constructed parabolic Ms profile was matched to measurement.

Uncertainties in the measurements from ion and electron temperatures and radial location of plasma density peak could explain discrepacies between experiment and theory at Rm=8 (a) Effect of uncertainty in Te (baseline Te=0) shown for 0< Te< 0.4 Ti. Measured at edge: Te=0.1 Ti. Ms=u/[k(Ti+Te)/mi]1/2 (b) Effect of uncertainty in the skewedness of the plasma density profile (baseline peak at r =17 cm) shown for r =10 cm and r =25 cm. Value of n depends whether radial location of measurement includes the peak or not. (c) Effect of 20% instrumental error in measuring Ms a b c d baseline (d) Effect of overestimation of Ti using Doppler broadening technique and spatial deconvolution of 5-chord measurement where size of radial layer is 1/5 of plasma cross-section, and from possible turbulent poloidal flow. Spectral lines have multi-Maxwellian shapes. Shown for 15 eV < Ti < 30 eV.

The possible presence of a partially ionized plasma mantle at the LGFS’s could lead to the overestimation of measured density ratio A partially ionized plasma mantle at the LGFS’s (from neutral penetration due to recycling, charge-exchange, and ionization) that could extend inward radially by approximately 2 cm (the penetration depth being roughly independent of z, while the distance between LGFS’s decreasing with z), could underestimate n2 by 20% and n1 by 40%.  n2/n1 could be overestimated by 30%. Spectral line intensity z=0 z=85 cm C2+ H Neutral penetration depth from charge-exhange and electron-impact ionization mfp=(CX-1+ ionize-1)-1 CX = 3.8 cm ionize= 3.5 cm  mfp = 1.8 cm 12 cm 19 cm

Conclusions The centrifugal confinement effect produced by the plasma rotation was determined from interferometric measurements of plasma density at the magnetic minimum (midplane) and 85 cm off-midplane, near the magnetic maximum. Complete time histories of density at these two locations were obtained and compared to deduce the efficacy of axial conffinement. Other parameters are also directly measured at midplane and off-midplane: rotation velocity profiles, ion temperature, and diamagnetic flux. Strong centrifugal confinement was observed, with average plasma density at magnetic minimum being over one order of magnitude higher than the density near the magnetic maximum. Strong plasma axial confinement lasts many momentum or energy confinement times (~ 100’s of s), in sharp contrast with the non-rotating plasmas in magnetic mirrors where axial confinement is lost on average on ion sound time scale (200 s). The observed scaling of the average density ratio at midplane and off-midplane was obtained as a function of the shape of the magnetic field (mirror ratio) and the data were compared with the Grad-Shafranov equation solution of the centrifugally confined density. The data were shown to be in agreement with the predictions of the ideal MHD equilibrium theory, confirming the prediction that strong axial confinement correlates with high plasma rotation velocity u and large sonic Mach number u/(T/m)1/2.