D.J. Schlossberg, D.J. Battaglia, M.W. Bongard, R.J. …pegasus.ep.wisc.edu/Technical_Reports/pdf/STW/DJS_STW09.pdfD.J. Schlossberg, 2009 Spherical Tokamak Workshop, Madison, WI Oct

D.J. Schlossberg, D.J. Battaglia, M.W. Bongard, R.J. Fonck, A.J. Redd

D.J. Schlossberg, 2009 Spherical Tokamak Workshop, Madison, WI Oct 2009

University of Wisconsin - Madison 1500 Engineering Drive

Madison, WI 53706

•  Concept Overview

•  Implementation on PEGASUS

•  Results

•  Current areas of investigation

•  Summary



•  Solenoid-free startup and ramp-up have been identified by FESAC as critical ST issues (FESAC TAP report)

•  Solenoid-free startup with point-source helicity injection significantly extends the PEGASUS operating space –  Saves limited Ohmic transformer flux –  May enable high-IN, high-β studies on PEGASUS

•  Point-source helicity injection is flexible –  Gun assemblies can be placed at convenient locations –  Presently being studied on PEGASUS (to date: Ip up to 0.17 MA)


•  Helicity describes linking of magnetic flux

•  Total helicity within a bounded volume €

K = 2ΦiΦ j

Φi

Φj

€

= AV∫ ⋅B d3x

€

K = Li, jΦiΦ jj=1

N

∑i=1

N

∑

Berger, M. Plasma Phys. Controlled Fusion 41, 1999

Current along B field = helicity Current drive = helicity injection


€

dKdt

= − 2 ηJ ⋅B d3xV∫ − 2∂ψ

∂tΨ − 2 ΦB ⋅ ds

A∫

•  Resistive Helicity Dissipation –  E = ηJ → much slower than energy dissipation (ηJ2) –  Turbulent relaxation processes dissipate energy and conserve helicity

•  AC Helicity Injection:

•  DC Helicity Injection: €

K•

AC = −2∂ψ∂t

Ψ = 2VloopΨ

€

K•

DC = −2 ΦBA∫ ⋅ ds = 2VinjB⊥Ainj

€

K = A +A vac( )V∫ ⋅ B −Bvac( ) d3xTotal helicity in a tokamak geometry:


•  Non-solenoid startup is a critical issue for future long-pulse STs •  Would extend efficiency of OH drive and provide j(R) modification on

present experiments that already have a central solenoid

•  Plasma gun point-source DC helicity injection tested on Pegasus •  Low impurity, high Jinj source •  Scalable design ⇒ flexible & compact

Anode

Gun Molybdenum Cathode

Molybdenum Cathode - Anode

Boron Nitride Washers

Molybdenum Washers

Anode

D2 gas

Vbias +

Varc +


N.W. Eidietis UW-Madison Ph.D thesis, 2007

Inboard Divertor Gun Injection Outboard Midplane Gun Injection

Anode Plate

Radial Plasma Guns

Axial Plasma Guns

Spherical Anode

Rgun = 16 cm, Zgun = - 75 cm Rgun = 70 cm, Zgun = - 20 cm

D.J. Battaglia UW-Madison Ph.D thesis, 2009


•  Conditions for relaxation to occur: •  Bv: low to allow null formation •  BTF: high to increase helicity injection •  Bv, BTF: tokamak equilibrium - force balance, qa •  Bv/BTF: avoid collision with injector hardware

•  Consistent with experimental observations •  divertor injection:

•  center-post limited discharges •  relaxation coincides with reversal of central

poloidal flux •  midplane injection:

•  model of perturbed magnetic field shows null in relaxed cases

60kA

40

20

0

Curr

ent

28x10-326242220

time (s)

200

100

0

-100cent

ral c

olum

n flu

x

20A151050

current multiplication

Ip Iinj

ψpol Ip/Iinj

Divertor injection

Midplane injection

See D.J. Battaglia, et al., J. Fusion Energy, 28 (2009) 140-3


€

M ≡ Iφ /IinjCurrent multiplication:

Open field line current M = G

Injected current perturbs vacuum magnetic field

Tokamak-like plasma M > G

Plasma expands inwards to fill the volume while connected to

guns

Limits dictated by helicity and Taylor relaxation

Decaying plasma

Stochastic magnetic fields “heal” into closed

magnetic surfaces


Helicity balance in a tokamak geometry:

€

dKdt

= − 2 ηJ ⋅B d3xV∫ − 2∂ψ

∂tΨ − 2 ΦB ⋅ ds

A∫

€

Ip ≤Ap

2πR0 ηVind +Veff( )

•  Assumes system is in steady-state (dK/dt = 0) •  Ip limit depends on the scaling of plasma confinement via the η term

€

Veff ≈NinjAinjBφ ,inj

ΨVbias

Taylor relaxation of a force-free equilibrium:

€

∇ × B = µ0J = λB

€

λp ≤ λedge

€

µ0IpΨ≤ µ0Iinj2πRinjwBθ ,inj

Assumptions: •  Driven edge current mixes uniformly in SOL •  Edge fields average to tokamak-like structure

Ap Plasma area fG Plasma geometric factor ITF Toroidal field current w Edge width €

Ip ≤ fGεApITFIinj2πRedgew

1/ 2


Estimated plasma evolution

Plasma guns

Anode

Relaxation limit

Helicity limit

Ip max

Time

ITF = 288 kA Vbias = 1kV Vind = 1.5 V Iinj = 4 kA w = dinj L-mode τe

•  Total “loop voltage” from relaxation and PF ramp

Recent experimental campaign: Testing utility and validity of this simple helicity/relaxation model


All three discharges have the same Iinj and Bv evolution

120 V

900 V

Vbias = 1200 V

Relaxation limit

•  With guns, need sufficient helicity (i.e. Vbias) to reach the relaxation limit1

•  Can confirm relaxation limit by adding OH drive as helicity source

1 D.J. Battaglia, et al., Phys. Rev. Lett. 102 (2009) 225003


€

∝ Iinj

€


1/ 2

•  At each R0, max. Ip achieved scales as Iinj

1/2

•  Kinj insufficient to drive some discharges to limit as plasma expands

•  Scan Iinj: 1 - 5 kA –  ITF = 288 kA –  3 plasma guns: defines w –  Assume plasma geometry (thus, εAp/Redge) fixed at given R0


•  Relaxation Ip limit ∝ ITF1/2

–  Supported by shot-to-shot comparisons

–  Factor of two range in ITF

•  Difficult to conclusively demonstrate scaling

–  Limited range of ITF that produce quality discharges

–  Plasma parameters depend on ITF •  Particle confinement decreases •  Energy confinement may decrease •  q is lower → different equilibrium

shape

Discharges with same Iinj, Vbias €

∝ ITF

€


1/ 2


Anode

3 guns

w

•  Relaxation limit predicted to scale as w-1/2 •  Data suggests w ∝ NgunDgun

–  Likely due to alignment of plasma guns with flux surfaces –  w may also be related to edge instabilities, turbulence, drifts, etc.

€

∝1w

€


1/ 2

•  Orientation of gun array matched to edge field alignment –  Re-orientation is equivalent to a reduction in current channel width –  Experiments show increased relaxation limit


Anode

3 guns

w

140

120

100

80

60

40

20

0

kA

0.80.70.60.50.4m

After alignment Before alignment


•  80 kA target handoff to OH drive

–  Best coupling achieved when OH drive applied shortly after gun turnoff

•  150 kA with 18 mV-s –  ~ 50% flux savings

•  Extending operation space - No significant MHD during

Ohmic phase - Unlike OH only, where large

scale n=1 activity limits plasma evolution

- Equilibrium reconstruction of gun created plasmas show very low li ~ 0.2-0.3, and hollow J(r)


Slower PF ramp Plasma detaches at 29.4 ms

Faster PF ramp Plasma detaches at 25.3 ms

After detachment, current drive is purely inductive and MHD activity is reduced.

Est

imat

ed

Est

imat

ed

•  What determines λedge and λp? •  Edge current measurements with probes •  Larger range of ITF to test scaling •  Re-tilted guns

•  How does τe scale with Ip? •  Thomson scattering •  Increase Vbias to achieve larger Ip

•  What determines Zinj? •  Filament path length and modeling

•  Tokamak-like plasma properties: Ti, Te •  Spectrometer, Thomson scattering


year I p

(MA)

0.0

0.1

0.2

2007 2008 2009 2010

single gun

three guns increased

TF, Vbias

0.3

new geometry larger guns

(Proposed)

•  Outboard midplane gun startup results show great promise

•  Ip ~ 0.17 MA achieved with simple 3-gun array and PF induction

•  Helicity & Relaxation limits being identified to guide design to higher current •  Simple dc relaxation-helicity conservation model describes

macroscopic scaling of current limit •  Many outstanding questions: λedge, Zinj, confinement, etc •  Full understanding at microscopic level (e.g.. Intermittent MHD) will

require deeper analysis (i.e. NIMROD)

•  Pegasus goal: ~0.3 MA non-solenoidal target & hand-off to RF heating & growth •  Allows validation of understanding for projection to larger facilities

(e.g.. NSTX up to MA)

Documents

D.J. Schlossberg, D.J. Battaglia, M.W. Bongard, R.J. …pegasus.ep.wisc.edu/Technical_Reports/pdf/STW/DJS_STW09.pdfD.J. Schlossberg, 2009 Spherical Tokamak Workshop, Madison, WI Oct