chapter+9.+plasma+heating

8/6/2019 Chapter+9.+Plasma+Heating

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Dolan Chapter 9 1

Chapter 9. Plasma Heating



Dolan Chapter 9 2

Ohmic – current flow through plasma.

Compression – by magnetic field, shock wave, or beam pressure

Wave heating – radio waves, microwaves, laser beams

Particle beam injecton – electron beams, ion beams, or NBI

Example: n = 1020 m-3, T = 10 keV, V = 200 m3.W = 1.5nk(Te+Ti) ≈ 100 MJ. Maybe 50 MW for about 10 s.

Desirable features:• High power flux, small ports in chamber walls

• High efficiency of generation, transmission

• Large fraction of energy absorbed in plasma• High power per unit generator

• Reliable operation for long times

• Easy maintenance

• Low cost per Watt.

Plasma Heating Methods



Dolan Chapter 9 3

Electrodes or magnetic induction can drive plasma current.Power dissipated per m3 is

For Zeff = 1 and L = 18,

Resistivity of copper at room temperature is about 2x10-8 Ω-m.

Ohmic Heating



Dolan Chapter 9 4

Increases of Resistivity η

Neutral atoms increase η by factor

Impurity ions increase Zeff and η

Toroidal geometry

Trapped particles

Turbulence νeff >> νei

Turbulence increases energy loss rates.

High E may cause electron runaway.

Ignition by Ohmic heating is possible with very high B,

but auxiliary heating is usually needed.



Dolan Chapter 9 5

me( ∂ue/ ∂t) = -eEװ + η Jװ װ - meueνen

If |eEװ| > | η

װJ

װ – meueνen | ,

electrons continue to accelerate up to very

high energies, sometimes MeV, then they are lost.

• The energy is wasted, instead of heating the

plasma.

• A large part of the plasma current may be

suddenly lost.

• The walls may be damaged.

Runaway Electrons



Dolan Chapter 9 6

Compression Time

Compression time τc << τE adiabatic, reversible.

Compression time τc

> τE

, energy losses, nonadiabatic.

Extremely fast compression (τc ~ 1 μs) shock wave,

intense irreversible heating.



Dolan Chapter 9 7

Shock waves may be caused by rupturing a diaphragm

between gases at different pressues, by detonationof an explosive, or by motion of a piston (such as an

airplane wing) through the gas.

(a) nA > nC cs(nA) > cs(nC)(b) Top of density hill nA moves faster than bottom nC

(c,d) Slope n(x) gets steeper, forming a clif f.

Causes sudden, irreversible heating of the gas.

“Overturning” of the wave is limited by heat conductionand viscosity. Thickness ~ several λ (collisions).

Shock Waves in Gases



Dolan Chapter 9 8

Shock Waves in Plasmas

Caused by increase of wave speed with density.

May be large-amplitude MHD wave

Initiated by changing E or B in μs.

Electrodes or pulsed coils can induce sudden J.High J flowing in wave front magnetic piston,

like a snow plow.

Sometimes λ(collisions) >> shock front thickness.“collisionless shock wave” good ion heating (~10 keV)

Problems Low inductance, high voltage circuits required.

Coils and insulators close to plasma damaged by neutrons.

Cyclic stresses cause fatigue failures, limit coil B field.



Dolan Chapter 9 9

Ni = total number of ions = constant

N = number of degrees of freedom during compression.

1D compression γ = 3; 2D γ = 2; 3D γ = 5/3.May be different in parallel and perpendicular directions

Only the energy component in the direction of compressionis affected. If collisions equalize Te and Ti, then γ = 5/3.

Adiabatic Compression



Dolan Chapter 9 10

Compression of Toroidal Plasma

Initial plasma Compressed alongMinor radius

Compressed along

Major radius



Dolan Chapter 9 11

In low-beta plasma particles are tied to B lines

Compression of Toroidal Plasma

L = 2πRo

In high-beta plasma

Compute volume change from these equations,Then compute pressure change from adiabatic

equation

or from the following Table.



Dolan Chapter 9 12

Types of Toroidal Compression



Dolan Chapter 9 13

Compression in Tokamaks

Toroidal flux conservation Bta2 = constant

Bt = BoRo/R

If Bo constant during compression, then

a2/R = constant

Decrease of R (with constant Bo) also causesa compression of minor radius a.

Slow compression is non-adiabatic, need transport equations.

Experiments with the Adiabatic Toroidal Compressor (ATC)

Tokamak demonstrated effectiveness of compression.

Disadvantages: plasma shape control is complex,

Space available in chamber limits volume change,

Compression coils may be damaged by fatigue and neutrons.



Dolan Chapter 9 14

Compression in Tokamaks



Dolan Chapter 9 15



Dolan Chapter 9 16

Charged Particle Beam Injection

Charged particles cannot cross B field easily.

Can inject along B into open magnetic systems, but they

may be quickly lost out the other end. Beam-plasma

instability may extract electron beam energy and

heat the plasma (keV temperatures achieved).

Can inject electron beam into a torus by gradually

Increasing B.

High power electron or ion beams can compress inertial

confinement targets, causing heating.

G



Dolan Chapter 9 17

Plasma gun acceleratesPlasma blob to high u, n,

and Ti.

Gun plasma can be

injected into a tokamak.Charge-separation E field

helps plasma to penetrate

across B.

“Plasma focus” is collapseof plasma blob to small

diameter. Used as source

of x-rays or neutrons.

Vortex filaments observed.“Washer gun” = stack of Ti

washers impregnated with

Deuterium. Pulsed current

Ionizes and accelerates D+.

Plasma Guns



Dolan Chapter 9 18

RACE Device, Livermore

Plasma gun v = 106

m/s



Dolan Chapter 9 19

Tokamak de Varennes, Canada

Plasma gun v ~ 2x105 m/s



Dolan Chapter 9 20

Accelerator

BeamTransport

Tube

Plasma

Neutralizer Beam

Dump

Ions

Neutrals

Neutral Beam Production

SeparationMagnet

N t l B I j ti (NBI)



Dolan Chapter 9 21

Energy too high

Energy too low

Energy satisfactory

Neutral Beam Injection (NBI)

r

N t l B I j ti (NBI)



Dolan Chapter 9 22


Unattenuated beam densitynb(x) is trapped at a rate

where λa = attenuation length.In a uniform plasma

From graph, D at 100 keV

neλa = 3x1019 m-2.

If ne = 1020 m-3, thenλa = 0.3 m. Te = 10 keV (smooth curve)

Te = 1 keV (dashed curve)



Dolan Chapter 9 23

r dr

NBI

Ne tral Beam Injection (NBI)



Dolan Chapter 9 24


Ions trapped in dx at r will quickly fill volume (2πRo) 2πrdx.Ions deposited at small r will have greater effect on the

local density.

Let λav = λ evaluated at <ne> and <Te>.Then

λav > a/4

may give adequate penetration.

Example: ne = 8x1019 m-3, a = 1.0 m. nea = 8x1019 m-2.

Require neλav > 2x1019 m-2. Required Wo ≈ 70 keV.




Dolan Chapter 9 25

Neutral Beam Injection (NBI)May heat plasma to ignition

at small r, then expand to

full size.

Example: Ro = 10 m, Bt = 4.2 T

Elongation b/a = 1.6, ao = 1.4 m,neo = 1020 m-3, Wo = 150 keV

P = 130 MW

Final plasma a = 2.5 m

I = 8 MA.

Result depends stronglyon transport model,

alpha confinement,

alpha energy transfer to

electrons and ions.

b

a

Ti

DuoPIGatron Ion Source



Dolan Chapter 9 26

DuoPIGatron Ion SourcePenning discharge = cylinder

with axial magnetic field andnegative cathodes at the ends.

One cathode emits electrons,which bounce back and forth

between the end cathodes,

gradually diffusing to the

cylindrical anode, and ionizing

the neutral gas.

At extraction grids needuniform plasma density and

low B, to minimize transverse

energy and beam divergence.

22 cm diameter

A = anode

F = filaments

M = magnet coils

LBL Ion Source



Dolan Chapter 9 27

LBL Ion SourceLBL ion source uses B = 0, higher arc current.

p ~ 1 Pa.

Gas efficiency = (ion flow rate)/(flow rate of ions + gas)

30% (for LBL source) and 50% (for DuoPIGatron).

Need very powerful vacuum pumps.High gas flow can cause problems in accelerator,

beam transport tube, and in plasma (hot ion loss by charge

exchange.)70% D+ (full energy)

20% D2+ (1/2 energy per atom)

10%D3

+

(1/3 energy per atom)

Tokamak Fusion Test Reactor

(TFTR) extraction area 10x40 cm

120 keV, 65 A per source.

Accelerator Electrodes, LBL Source



Dolan Chapter 9 28

Accelerator Electrodes, LBL Source

Acceleratinggrid

deceleratinggrid

Accel-Decel design minimizes beam divergence angles

(0.5 degree parallel to slits, 1.3 degree perpendicular toelectrodes). Water-cooled grid rails fastened at one end only,

to allow thermal expansion. J ~ 3 kA/m2 attained.

If sparking occurs, high voltage must be switched off immediately.

TFTR Neutral Beam Injector



Dolan Chapter 9 29

5 x 7 m

TFTR Neutral Beam Injector

0.2 T Magnetic field shieldedby steel to avoid damaging

plasma confinement.




Dolan Chapter 9 30

Neutral Beam Injection (NBI)Fraction of ion beam neutralized by charge exchange

σ10 = neutralization by cx σ01 = reionization

If

Neutralization efficiency

Low efficiency for D+

above 100 keV.

Need 1 MeV negativeIon beams for ITER.

TFR Neutral Beam Injection (NBI)



Dolan Chapter 9 31

j ( )

Per MW of Do

Four units 20 MW (Do)

Pulse length = 0.5 s

Beam Duct and Pumping



Dolan Chapter 9 32

Beam Duct and Pumping

Cryogenic pumps remove neutral gas to keep it from enteringPlasma. Fast shutter valve closes after pulse ends.

Injection angle variable.

Neutral gas in beam duct some reionization.

Minimize PotLd/C. Po = 5 MW, t = 0.5 s, Ld = 2.5 m, C = 150 m3

/s.

Efficiency. Without recovery of unneutralized beam energy,

Efficiency = beam power/input power = 1.58/3.2 = 49%.

With recovery at 30% efficiency, net efficiency = 58%.

NBI Design Considerations



Dolan Chapter 9 33

Current density – maximize J, high φ, narrow gaps

High voltage breakdown – smooth electrodes, large gaps

Beam divergence angle – accel-decel electrodes, computer design, precise alignment, allow thermal expansion

Beam blowup – use narrow beamlets; put neutralization cellclose to accelerating grids

Overheating – cooling by water, helium, or liquid metal.

Arc damage – computerized diagnostics, fast circuit-

interrupters on power supplies.





Dolan Chapter 9 34


Electrode sputtering (surface erosion by ion bombardment) --Minimize neutral gas pressure in grid region.

Radiation damage – put electrodes far from reactor, out of

line of sight of plasma (bending magnet in between)Shield insulators from neutrons.

Gas flow – use cryogenic pumping system and fast-closing

valve.Long-pulse operation

Efficiency – convert energy of unneutralized ions into

electricity in beam dump.

Reliability and maintainability – ability to repair quickly

Cost

Wave Heating



Dolan Chapter 9 35

Coupling effective near

plasma resonances or

chamber resonances.

Waves need to penetrate

Inside before absorption.

E װ B = “ordinary mode”

Reflected at ω = ωpe

Wave Heating

Example: At n=1020 m-3,

What frequency O-mode

is required for penetration?ν= ωpe/2π = 90 GHz.

“Extraordinary mode” may

penetrate further.

Resonant Frequencies



Dolan Chapter 9 36


Coupling of wave energy to plasma is strong near resonances

Electron cyclotron frequency

Ion cyclotron frequencyLower hybrid frequency

Upper hybrid frequency

where

(rad/s)




Dolan Chapter 9 37


νce = ωce/2π

When B = 5 T and n = 1020 m-3, these frequencies are

Mode conversion can change the wave type.

Cavity Resonances



Dolan Chapter 9 38

Cavity Resonances

wave

Cavity Resonances



Dolan Chapter 9 39

Weakly absorbed waves can pass through the plasma

many times, reflecting from the chamber walls. If the wave

frequency or wavelength is tuned to a natural resonance

frequency of the plasma-filled chamber, then the wave

amplitude can become very large. (Like resonance of a

musical instrument) Changes of plasma density change

the resonant frequencies of the toroidal cavity. Thegenerator needs to follow the changing resonant frequency.

(Mode tracking).

The usually low impedance of the (plasma+chamber)becomes high near a resonance, improving the coupling

efficiency. Need smooth, high-conductivity walls.

Cavity Resonances

Wave Heating Methods



Dolan Chapter 9 40




Dolan Chapter 9 41


Ion Cyclotron Range of Frequencies (ICRF)



Dolan Chapter 9 42

Example: NUMAK reactor:

Cavity-backed aperture antennafor ion cyclotron range of

frequencies (ICRF)

Transmission line & cavitycoupling efficiency 97%

High voltage transformer

efficiency 85%

Generator/amplifier efficiency 75%

Net efficiency 59%

Good ion orbits needed.ICRF impuritiesincreased Prad,

possible MHD instabilities

NUMAK design

Radiofrequency (rf) Wave Heating



Dolan Chapter 9 43

Radiofrequency voltages ~ 30 kV, avoid breakdownPlasma near antenna & windows may facilitate arcing

Rapid shutoff of generators if arc occurs

Radiation damage to antennasVacuum windows outside neutron shielding

Need alloys with high conductivity after neutron irradiation

Waveguide bends reduce neutron streamingAdvantages of radiofrequency (rf) wave heating:

• Good efficiency

• NBI gas inflow and cryopumps avoided

• Smaller ports required for injection of rf or microwaves• Lower cost than NBI

Tokamak plasma current drive by rf, LH, ECH, or NBI

Radiofrequency (rf) Wave Heating

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