Measurements of plasma jets and collimated flux tubes that ...iccworkshops.org/icc2006/uploads/44/bellantalk_icc_2006_austin4b.… · build simplest relevant system, follow fast-scale

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