Measurements of plasma Measurements of plasma jets and collimated flux jets and collimated flux
tubes that are the tubes that are the precursors of precursors of spheromakspheromak
selfself--organizationorganizationP. M. Bellan, Caltech
ICC2006 –Austin
Coauthors: S. You, G. Yun, D. Kumar
Taylor Relaxation:
“magical process” where B self-organizes into axisymmetric configuration with closed flux surfaces
Initial ill-definedmagnetic field configuration
Relaxation:Linked toroidal and poloidal magnetic field
Axisymmetric confinement configurationJ.B. Taylor
How does this work??
1) How did initial plasma get in?
2) How does magnetic topology evolve?
3) What about axisymmetry?
Goal of Caltech programis to help answer these questions
How does the magic work?
Method:build simplest relevant system, follow fast-scale dynamics,develop models consistent with observations
Main results from before(experiment, ‘gobble’ model)
1. (JxB)z force drives axial plasma flow from wall (i.e., plasma sucked from wall, ingested, gobbled)
2. Mass source required at wall (mass to be ‘gobbled’)
3. Ingested plasma convects frozen-in toroidal flux
4. Flux pile-up amplifies Bφ, collimates flux tube (pinching)
5. At critical length, collimated flux tube kinks
6. Kink converts toroidal flux to poloidal flux
New resultsA. Measurements supporting ‘gobble’ model:1. Pre-breakdown neutral profile unrelated to plasma profile
• Movable fast ion gauge probe measures pre-breakdown neutral gas profile
2. Fast jet • Doppler spectroscopy shows velocity is 10’s of km/s
3. High, localized plasma density • 1022 to 1023 m-3 via Stark broadening, confirmed by HeNe interferometer• axial pile-up of density observed
B. ‘Gobble’ model implications for kink/sausage− βφ =1 prediction provides ‘missing link’ for kink/sausage theory- paramagnetism balances diamagnetism - dynamics follows trajectory in 2D kink/sausage parameter space
Experimental Setup
Copper annulus 50.8 cm diam
Copper disk 20.3 cm diam
Gas nozzles
Coaxial, co-planar electrodes
Bias field coilmakes linked magnetic flux
Gas puff valve(typical)
Gas nozzle
50 cm
disk
annulus
Side View
disk
annulus
Installation
Sequence
highvacuum
Bias field
Puff in neutral gas(new result: fast ion gauge measurement confirms this picture)
Breakdown, “spider leg formation”
Spider leg Gas source
Spider legs get bigger
Spider legs merge to form central column
Central column lengthens
I ~ 100 kA
Scale of experiment
Question: Where does plasma come from?
Vacuum here initially,no gas
Toroidal flux injection and helicity injection• gun current I creates toroidal flux
• voltage V across electrodes is rate at which this toroidal flux is injected– coil creates poloidal flux Ψ linking toroidal flux– helicity injection rate is 2VΨ
I
Bφ
The need to gobble plasma
• toroidal flux is frozen into plasma– toroidal flux injection necessarily involves
plasma injection
• need source of plasma: gas nozzle is where ingested plasma comes from
• an MHD-driven ‘pump-in’
Collimation
Spider leg Gas source
Collimatedflux tube
Gas source
Collimatedflux tube
Amplification of convected toroidalflux density due to axial compression
Toroidalflux
Flux conserved during compression of a fluid element
Same toroidal flux as before
poloidal flux linked by toroidal fluid element is invariant
Poloidal current I linked by toroid must also be invariantsince I I
sB dpol ⋅= ∫ψ
closed material line
∂B∂t rBpol∇
Ur − rUpol∇
Br − B∇ Upol
Toroidal component of induction equation (exact)
0≈φU since current is constant
ddt
Br −
Br ∇ U
Negative divergence implies Bφ amplification i.e., converging flow increases pinching
re-write as
Toroidal field grows in proportion to mass accumulation in jet frame
Involves flow, compressibility, and frozen-in flux
induction
continuity
ddt
Br −
Br ∇ U
∇ U − ddt
ddt
Br 0
• Pile-up of flow amplifies Bφ
• Ampere’s law gives 2πrBφ=μ0I
• since I is fixed, r decreases
• central bulge reduced, get collimation
Cartoon showingpile-up of toroidal fieldlines convectedwith flow
Frozen-inconvectingtoroidal magneticfield lines
Consequences for βφ and β
• (JxB)z drives flow with
• flow thermalization gives
• i.e.,
vz ≈B0
vTi ≈B0
nTi
B2/20≃ 1
vTi ≈B0
nTiB 2/20
B2
B2 a2
Flow velocity B/ 0 becomes thermalized so
implies
Bz220 plasma
Bz2
20 vac
Flow thermalization gives
Corresponding to
MHD equil’n
cancel
result
vTi ≈B0
nTi
B2 /20≃ 1
P Bz2
20 plasma
B2
20 Bz
2
20 vac
Implies paramagnetism equals diamagnetism(analogy: βθ ~1 in a tokamak)
Implication for sausage/kink theory
• cylindrical sheet current stability condition
|k|aB̄ 0pz2I|m|I|m|′
mkaB̄0vz2
|k|a −K |m|K |m|′ 1 stable
Flow thermalization implies these fields are same
High density, sausage
• MHD flow fills up flux tube filament connected to wall gas source
• Can get very high densities, n=1022 -1023 m-3
• High density seems related to sausage modes
• Sausage related to breaking off, reconnection of filamentary flux tube
Shot #7211: H, 70psi, 6 kV, Vbias=190 V
B-dot array
electrodes
4.0 μs 5.4 μs 6.8 μs 7.5 μs
stable column kinked detached
stable column kinked detached
stable column kinked detached
stable column kinked detached
stable column kinked detached
stable column kinked detached
stable column kinked detached
Example of Doppler shift measurement of
jet velocity,Stark broadening measurement of
density
x
y
Line of Sight (top view)
Axis of chamber
~33o
electrodes
The fiber array is moved by about 4 mm at a time. (w.r.t. the electrode plane)
• vertical distance from the foot-point to the apex = 40 mm• diameter of foot-point = 3/8’’~ 9.5 mm• diameter of the circle surrounding foot-point = 1.25’’ ~ 32 mm• diameter of the plasma arch is about 20 ~ 30 mm
The spacing between adjacent fiber channels is ~ 4 mm, the total span of the fiber array being 4*11 = 44 mm.
ch1ch12
Shot range = #4577-4606Gas = Argon, 60 psiVgun = 6.0 kVVgas = 450 VVbias = 200 VGate (camera) = 0.5 – 0.53 μs after breakdownGate (spectrometer) = 0.35 – 0.65 μs after breakdown
anode, S-pole
cathode, N-pole
Red – reference lineThe other colors correspond to measurement point on the plasma arch as shown in the left.
black - #4586-ch3blue - #4591-ch7light blue - #4602-ch9
Raw spectra MaxEnt-deconvolved spectra
• Vertical axis: normalized intensity• Horizontal axis: pixel number
512 517 522 527
0.2
0.4
0.6
0.8
1
512 517 522 527
0.2
0.4
0.6
0.8
1
−36 −24 −12 0x @mmD
0
10
20
30
40
50
60
y@
mmD
11 9 7 5 3 1channel #
Map of Signal Intensity
This intensity map confirms that the fiber array followed the plasma arch correctly; its horizontal span covered the entire arch and it collected sufficiently many data points across the arch.
Map of Doppler Shift
−36 −24 −12 0x @mmD
0
10
20
30
40
50
60
y@
mmD
11 9 7 5 3 1channel #
cathodefoot-point
apex(center of arch)
Line of sight effect is not taken into account in this map.
Brighter the more blue Doppler shifts.Doppler velocity gets bigger near the apex.Doppler shifts are greater on the left side of the
arch than on the right side.
10 20 30 40 50y @mmD
0
2
4
6
8
relppoDstfihs@
mkê
sD
0 10 20 30 40 50y @mmD
0
20
40
60
yticolev@
mkê
sD
Doppler Velocity (apparent)Doppler Velocity (line-of-sight corrected)
Foot-point (red cross) is at y=40 mmApex (green cross) is at y=0 mm
Line of sight angle at a vertical position (y) is determined by approximating the plasma arch as a second-order polynomial curve.
4330 4335 4340 4345 4350WaveLength @ÅD
-0.2
0
0.2
0.4
0.6
0.8
1
ytisnetnIH
dezilamronL
Doppler Shift HHγ; center electrode LStark broadening (Hγ)
Example of Stark broadening density measurement(Spheromak gun)
•spectrum below the Hγ spectrum is the reference Dγ lines.•spectrum taken from central column jet • Stark width corresponds to n ~ 2x1022 m-3
Now under construction
• 60 kJ pulse forming network– 10x stored
energy, flat-top– will extend pulse
length five-fold– should give 5x
longer jet – further insight into
spheromakformation
Measurements of plasma jets and collimated flux tubes that are the precursors of spheromak self-organization How does this work??Goal of Caltech program�is to help answer these questions� � �Method: �build simplest relevant system, �follow fast-scale dynamics,�develop models consistent with observations ��Main results from before�(experiment, ‘gobble’ model)New results Experimental SetupSide ViewInstallationSequence Puff in neutral gas�(new result: fast ion gauge measurement confirms this picture)Breakdown, “spider leg formation”Spider legs get biggerSpider legs merge �to form central columnCentral column lengthensScale of experimentQuestion: �Where does plasma come from?Toroidal flux injection and helicity injection The need to gobble plasmaCollimationConsequences for bf and bImplication for sausage/kink theory High density, sausageExample of �Doppler shift measurement of� jet velocity,�Stark broadening measurement of density�� Now under construction
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