Plasma break-down, ramp-up andPlasma break-down, ramp-up andflux consumptionflux consumption

D. Mueller

January 26-28, 2010

Culham Sci CtrU St. Andrews

York UChubu UFukui U

Hiroshima UHyogo UKyoto U

Kyushu UKyushu Tokai U

NIFSNiigata UU Tokyo

JAEAHebrew UIoffe Inst

RRC Kurchatov InstTRINITI

KBSIKAIST

POSTECHASIPP

ENEA, FrascatiCEA, Cadarache

IPP, JülichIPP, Garching

ASCR, Czech RepU Quebec

College W&MColorado Sch MinesColumbia UComp-XGeneral AtomicsINLJohns Hopkins ULANLLLNLLodestarMITNova PhotonicsNew York UOld Dominion UORNLPPPLPSIPrinceton UPurdue USNLThink Tank, Inc.UC DavisUC IrvineUCLAUCSDU ColoradoU MarylandU RochesterU WashingtonU Wisconsin

NSTXNSTX Supported by

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NSTXNSTX NSTX-PAC-25 – Solenoid Free Start-up (Mueller) February 18-20, 2009

Break-down and start-up receive little attention unless they fail to reliably provide a plasma

Break-down, Ip < 10 to 20 kA

Start-up, 10 kA < Ip < 100 kA

Controlled ramp-up Ip > 100 kA• Central solenoid, OH, provides

voltage• PF5 provides vertical field to

control plasma radius• Other PF coils - shaping• Gas and NB provide fueling and

heating• Feedback control of coils begins

with controlled ramp-up

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NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Plasma Breakdown

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• The central solenoid called OH for Ohmic Heating coil on NSTX is supplied with a current in the positive sense (counter-clockwise when viewed from above) before T0

• At T0, the current is reduced towards zero by action of the rectifiers (aided by the IR drop in the coil)

EBB

€

V = −dΦ

dt= −

d

dtB ⋅dA∫∫

•Electric field accelerates free electrons along toroidal field•Free electrons are always present, but can be supplied by ECH, radiation, heated filaments, etc.•Vessel is filled to some pressure p with D2

Leakage field

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Breakdown in a gas

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The Paschen curve for dry air, nitrogen, and hydrogen. (from J. D. Cobine, Gaseous Conductors, Dover, 1941)

• Breakdown physics (for fixed magnetic geometry) can be summarised by the Paschen curve which determines the Electric field for breakdown for a given fill pressure

• Can be determined from mean free path arguments

€

F = mdv

dt= qE ⇒ v impact =

q

mEt

0

τ coll

=qE

mnσv impact

⇒

1

2mv impact

2 = qEλ ≥ E ion =13.6eV (Hydrogen)D. Gates

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

The breakdown of a gas can be understood by applying a simple kinetic theory model to the collisions

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• Density of electrons ne with velocity v driven by an electric field through gas density of n0 and collision cross section c, for low n0 – dne/dt = ne n0 c v : n0 c v is the collision rate

– mean free path, c = 1/(n0 c )– If Ee > 13.6 eV, ionization can occur

• For parallel plate electrodes– If an electron produces new electrons

per meter then– dne = ne dx– ne = ne (0) ex

is called the first Townsend coefficient– The 2nd Townsend coefficient describes

secondary emissionS.C. Brown, Intro. To Electrical Discharges in Gases, John Wiley and Sons, 1966.

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

The First Townsend coefficient, is not a simple function of E and p, but /p is

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•For NSTX, p ~ 1.5 to 2.5 x 10-5 Torr GP, and Vl ~ 1.6 to 4 V/turn

−E ~ 0.1 to 8 V/m (R is 0.2 to 1.4 m)

−Typically Vl ~ 2.2 V, p ~ 6 x 10-5 Torr

−E/p ~ 0.6 x 10 4 V m-1Torr-1 /p ~ 70 (m Torr)-1 at R = 1m−E/p ~ 2.0 x 10 4 V m-1Torr-1 /p ~ 250 (m Torr)-1 at R = 0.3 m−For NSTX then about 4.2 to 13 x 10-3 new electrons/m

•Electrons must travel a long way before being lost

R. Papoular, Nuclear Fusion 16 (1976) 37.

For E/p > 104 V m-1 Torr-

1), Te is high enough that thermal ionization becomes increasingly important and limits Te to about 10eV until ionization of the initial gas is nearly complete

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Electrons must travel many ionization lengths before being lost if an avalanche is to occur.

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• Ionization length ~ 80 - 250 m•The stray field connection length, L ~ h BT/<Bz> where h is the height of the machine and <Bz> is the average transverse field

−For NSTX B ~ 4 kG, h ~ 2 m

− <Bz> ~ 2.5 to 5.0 G

− L ~ 1.6 to 3.2 km−6 to 40 ionization lengths (more near R= 0.3 m)

• The electron drift velocity, vd, In H2 is approximately 35 E/p (m/s)

−Characteristic ionization time, ( vd)-1 ~ 10 to 110 s − ~ 2 -15 ms to wall

Field null at start-up in NSTX, includes eddy currents

D. Gates

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Sufficient E/p is needed to get avalanche but what happens as E/p increases?

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• Diffusion ~ 5 x 104 E/B2 (m2/s)– 10 keV limit (at E/p ~ 1 x 104) means max ~ 5 x 106 p/B2 (m2/s)− Loss rate D/a2 ~5 x 10-4 /s , Diffusive loss time is thousands of s

• Toroidal drift due to transverse velocity– v = 7 x 10-5 (E/p)/(RB) (E/p+ 4 x 104)– Increases with (E/p)2: at 2.0 x 104 V m-1 Torr-1, v ~ 20 m/s– Loss time a/v ~ 200 ms, but drops with increasing (E/p)2

• If pressure is too low, pd will not be thick enough to provide electrons for the avalanche to continue

• All above taken together– Standard NSTX start-up conditions– VL = 2.2 V/turn with stray fields below 5 G over much of the

vessel– p = 6 x 10-5 Torr (actual) (+/- 3 x 10-5 Torr)– E/p ~0.7 to 2.2 x 104 V m-1 Torr-1

– Time for avalanche to occur ~ 1-2 ms with Te ~ 10 keV

Gauge factor for D2 is 2.88

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Avalanche phase ends when electron-neutral collision rate = electron-ion collision rate

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•Rates are equal when ne ~ 0.1 n0

•Current density is J = n0 e v where is the ionization fraction

= 3.95 x 105 E (A m-2) ~ 40 kA m-2 (near CS)

Ip = 5 - 10 kA

−For Ip= 5 kA at .4 m, the poloidal field is about 0Ip/2a ~ 50 G−Sufficient to overcome the effects of stray fields, Grad B and curvature drifts.

•When ionization is nearly complete, Te increases above 10 keV and is then limited by low Z impurity radiation to ~ 30 keV until they are ionized

−This is often a sticking point when either impurities generated from the wall or the density is too high

−For NSTX this can happen at Ip = 20 to 80 kA and limits the current start-up

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Too high prefill (low E/p) breaks down but fails to start Ip up, too low prefill (or low fueling) gives higher Ip, but instabilities

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•Too high prefill raises H and C radiation•Causes Ip to not reach target of 90 kA at 20 ms

•Too low prefill does not cause discharge to fail to break-down•2x10-6 is enough to make plasma (zero does fail)•Low p has H spikes associated with MHD

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Controlled ramp-up

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•At 20 ms after Ip > 90 kA, the plasma current, outer gap and vertical position are controlled by feedback•At 70 to 200 ms when Ip > 300 kA, the plasma boundary from rt-EFIT is used to provide feedback•dIp/dt is chosen to

1) minimize resistive flux consumption before Ip flat-top starts

2) avoid deleterious MHD, practically dIp/dt ≤ 4 MA/s after .3 s

•Two examples of plasma growth strategies: • A) Grown in size so as to keep qedge ~

constant • B) Size of the plasma can be maximized as

early as possible

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Growth strategies

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•Constant q growth realizes fully evolved J(r) profiles earlier and has higher internal inductance, li

•Full aperature scenario has broader J(r) and minimizes li

•Each strategy is affected by impurities, bootstrap current drive, and heating power and timing in ways beyond the scope of this talk

~ 25 ms~ 100 ms~ 175 ms~ 250 ms

~ 25 ms~ 100 ms~ 175 ms~ 250 ms

135684104215

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Volt-second (flux) consumption

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NSTX seldom runs with no auxiliary power so data for purely inductive flux consumption is sparseMenard, Nucl. Fus. 41 (2001) summarizes early NSTX results

€

ΔΦR (t) =dt'

IpJφ∫ EφdV

0

t

∫

€

−ΔΦS (t) ≡ VS0

t

∫ dt '= ΔΦI (t) + ΔΦR (t)

where

ΔΦI (t) =dt'

Ip

∂

∂t∫ BP

2

2μ0

⎛

⎝ ⎜

⎞

⎠ ⎟dV

0

t

∫

Total poloidal flux

€

CE ≡ ΔΦR /μ0R0Ip

Ejima coefficient

Φ Computed at the end of the Ip ramp

Ejima - Wesley coefficient

€

CE−W ≡ ΔΦI + ΔΦR( ) /μ0R0Ip

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

Summary

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•Scenario with low stray fields exists over much of vessel volume•Loop voltage of 2V/turn is adequate to break-down prefill gas of 5.5 x 10-5 Torr•Low Z impurities or too high prefill prevents Ip ramp=up•Too low gas fueling (low prefill and no early gas puff) leads to MHD•Typical ramp-up has a goal of keeping li low•NSTX is starved for V•s but can reach 1 MA ohmically with a short flattop

NSTX Physics Operations Course Start-up (Mueller) Jan 26-28, 2010

VISUAL SUMMARY

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