1. 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

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

3. MCX schematics and plasma parametersV
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.

4. 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

5. 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 ~ s
Measured momentum
confinement time
m ~ 500s
No “major disruptions” 
MHD Stable?

6. 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

7. 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

8. 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).

9. 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.

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

11. 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).

12. 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.

13. 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.

14. 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= 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

15. 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.