Heating, Current Drive Heating, Current Drive Ohmic heating - - PowerPoint PPT Presentation

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Heating, Current Drive Heating, Current Drive Ohmic heating - - PowerPoint PPT Presentation

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Heating, Current Drive Heating, Current Drive Ohmic heating Compression Charged particle injection Neutral beam injection Neutral beam injection Wave heating Ion cyclotron frequencies Electron cyclotron frequencies Electron cyclotron

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Heating, Current Drive Heating, Current Drive

Ohmic heating Compression Charged particle injection Neutral beam injection Neutral beam injection Wave heating Ion cyclotron frequencies Electron cyclotron frequencies Electron cyclotron frequencies Lower hybrid frequency Profile Control

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ITER Heating Methods g

microwaves

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Ohmic current flow through plasma

Plasma Heating Methods

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 NB I Example: n = 1020 m-3 T = 10 keV V = 200 m3 Example: n = 1020 m 3, T = 10 keV, V = 200 m3. W = 1.5n(T

e+Ti) ≈ 100 MJ. Maybe 50 MW for about 10 s.

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SLIDE 4

Desirable Features

power flux, small ports efficiency of generation & transmission fraction of energy absorbed in plasma fraction of energy absorbed in plasma power per unit generator Reliable Easy maintenance Low cost per Watt.

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  • cost pe

att

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Ohmic Heating

Electrodes or magnetic induction can drive plasma current. Power dissipated per m3 is For Zeff = 1 and L = 18 For Zeff = 1 and L = 18, Resistivity of copper at room temperature is about 2x10-8 -m.

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Increases of Resistivity 

Neutral atoms increase  by factor Neutral atoms increase  by factor Impurity ions increase Zeff and  Toroidal geometry Trapped particles Turbulence  >>  Turbulence eff >> ei Turbulence increases energy loss rates. High E may cause electron runaway High E may cause electron runaway. Ignition by Ohmic heating is possible with very high B,

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but auxiliary heating is usually needed.

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Runaway Electrons

me( ∂ue/ ∂t) = -eEװ+ װJ װ- meueen If |eEװ| > | װJ װ– meueen | , electrons continue to accelerate up to very high energies, sometimes MeV, then they are lost. The energy is wasted instead of heating the

  • The energy is wasted, instead of heating the

plasma.

  • A large part of the plasma current may be

g p p y suddenly lost.

  • The walls may be damaged.

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Compression

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Compression Time

Compression time c << E adiabatic, revesible. Compression time c > E, energy losses, nonadiabatic. Extremely fast compression ( ~ 1 s)  shock wave Extremely fast compression (c ~ 1 s)  shock wave, intense irreversible heating.

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Rupturing diaphragm between gases at different pressues

Shock Waves in Gases

Rupturing diaphragm between gases at different pressues Detonation of explosive Motion of a piston (airplane wing) through gas. Causes sudden, irreversible heating of the gas. “Overturning” of the wave is limited by heat conduction and viscosity. Thickness ~ several  (collisions).

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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 s. Electrodes or pulsed coils can induce sudden J, B. High J flowing in wave front  magnetic piston, like a snow plow. “collisionless shock wave”  good ion heating (~10 keV)

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Shock Wave Heating Shock Wave Heating

P bl Problems Low inductance, high voltage. , g g Neutrons damage coils and insulators . Fatigue failures, limit coil B field.

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Adiabatic Compression

N = number of degrees of freedom during compression. 1D i  3 2D 2 3D 5/3 1D compression  = 3; 2D  = 2; 3D  = 5/3. May be different in parallel and perpendicular directions y p p p Only the energy component in the direction of compression is affected is affected. If collisions equalize T

e and Ti, then  = 5/3.

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Compression of Toroidal Plasma

C d l Initial plasma Compressed along Minor radius C d l Compressed along Major radius

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Compression of Toroidal Plasma

Compute Volume Change: low beta plasma low-beta plasma high beta plasma high-beta plasma Then compute change of Wi

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Compression in Tokamaks

Disadvantages: Plasma shape control is complex, Space available in chamber limits volume change, Compression coils may be damaged by fatigue and neutrons Compression coils may be damaged by fatigue and neutrons.

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P i I j i Partice Injection

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Charged Particle Beam Injection

Charged particles cannot cross B field easily. Along B into open magnetic systems, may be lost out other end. Beam-plasma instability extracts electron beam energy heats plasma  keV Can inject electron beam into a torus by gradually Increasing B. High power ion beams compress inertial confinement targets.

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Plasma Guns

Injected into a tokamak: Charge-separation E field Charge separation E field helps plasma to penetrate across B. “Plasma focus” is collapse

  • f plasma blob to small
  • diameter. Used as source
  • f x-rays or neutrons.

Vortex filaments observed.

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SLIDE 20

RACE Device Livermore RACE Device, Livermore

Plasma ring accelerator 0.1 mg plasma rings 40 kJ 20% efficiency 20% efficiency v = 106 m/s

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SLIDE 21

Tokamak de Varennes Canada Tokamak de Varennes, Canada

Pl 2 105 / Plasma gun v ~ 2x105 m/s

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Neutral Beam Injection (NBI)

Energy too low Energy satisfactory Energy too high r Energy too high

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Neutral Beam Injection (NBI)

Unattenuated beam density a = attenuation length. In a uniform plasma From graph, D at 100 keV nea = 3x1019 m-2. If n = 1020 m-3 then If ne = 1020 m-3, then a = 0.3 m. T

e = 10 keV (smooth curve)

T

e = 1 keV (dashed curve)

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T

e

1 keV (dashed curve)

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NBI Penetration ~ a/4

NBI a a/4

r

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Neutral Beam Injection (NBI)

Let av =  evaluated at <ne> and <T

e>.

av > a/4 may give adequate penetration. Example: ne = 8x1019 m-3, a = 1.0 m. nea = 8x1019 m-2. Require neav > 2x1019 m-2. q

e av

Required Wo ≈ 70 keV.

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Neutral Beam Production

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DuoPIGatron Ion Source

22 di t Penning discharge 22 cm diameter A = anode F = filaments B M = magnet coils e- Bz

  • 



  • 

e-    

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LBL Ion Source

LBL i B 0 hi h t 1 P LBL ion source uses B = 0, higher arc current. p ~ 1 Pa. Gas efficiency = 30% (for LBL source) , 50% (for DuoPIGatron). Powerful vacuum pumps. High gas flow  problems in accelerator, beam transport tube and in plasma (hot ion loss by charge beam transport tube, and in plasma (hot ion loss by charge exchange.) 70% D+ (full energy) 20% D + (1/2 t ) 20% D2

+ (1/2 energy per atom)

10%D3

+ (1/3 energy per atom)

TFTR extraction area 10x40 cm 120 keV, 65 A per source.

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Accelerator Electrodes, LBL Source

Accel Decel design minimizes beam divergence angles Accel-Decel design minimizes beam divergence angles (0.5 degree parallel to slits, 1.3 degree perpendicular to electrodes). Water-cooled grid rails fastened at one end only,

Accelerating decelerating

to allow thermal expansion. J ~ 3 kA/m2 attained. If sparking occurs, high voltage must be switched off immediately.

Accelerating grid dece e at g grid

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TFTR Neutral Beam Injector

0.2 T Magnetic field shielded by steel to avoid damaging plasma confinement.

5 x 7 m

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Neutral Beam Injection (NBI)

F ti f i b t li d b h h Fraction of ion beam neutralized by charge exchange 10 = neutralization by cx 01 = reionization If Neutralization efficiency Low efficiency for D+ above 100 keV. Need 1 MeV negative Need 1 MeV negative Ion beams for ITER.

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TFR Neutral Beam Injection (NBI)

P MW f Do Per MW of Do Four units  20 MW (Do) Pulse length = 0.5 s

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Beam Duct and Pumping

Cryogenic pumps remove neutral gas to keep it from entering

  • Plasma. 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%.

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C t d it i i J hi h 

NBI Design Considerations

Current density – maximize J, high , narrow gaps High voltage breakdown – smooth electrodes, large gaps g g g g p Beam divergence angle – accel-decel electrodes, computer design precise alignment allow thermal expansion design, precise alignment, allow thermal expansion Beam blowup – use narrow beamlets; put neutralization cell l t l ti id close to accelerating grids Overheating – cooling by water, helium, or liquid metal. g g y q Arc damage – computerized diagnostics, fast circuit- interrupters on power supplies

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interrupters on power supplies.

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NBI Design Considerations

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. Shield insulators from neutrons. Gas flow – use cryogenic pumping system and fast-closing valve. Long pulse operation Long-pulse operation Efficiency – convert energy of unneutralized ions into electricity in beam dump. Reliability and maintainability – ability to repair quickly Cost

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ITER Neutral Beams

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From Jean Jacquinot, SOFT 2008

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ITER NBI System y

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ITER NBI Systems

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From Jean Jacquinot, SOFT 2008

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Neutral Beam Injection

heating heating current drive rotation stability

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Heating by Electromagnetic Waves Heating by Electromagnetic Waves

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C li t l

Wave Heating

Coupling to plasma resonances or chamber resonances. chamber resonances. Penetrate before absorption. Eװ B = “ordinary mode” Reflected at  = pe Example: At n=1020 m-3 Example: At n=10 m , What frequency O-mode is required for penetration? = pe/2 = 90 GHz. “Extraordinary mode” may penetrate further

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penetrate further.

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SLIDE 42

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From H.P. Laqua, Karlsruhe Summer School 2008

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From H.P. Laqua, Karlsruhe Summer School 2008

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Cold Plasma Wave Propagation

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From H.P. Laqua, Karlsruhe Summer School 2008

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Resonant Frequencies

Coupling of wave energy to plasma is strong near resonances Electron cyclotron frequency (rad/s) Electron cyclotron frequency Ion cyclotron frequency Lower hybrid frequency ( ) Lower hybrid frequency Upper hybrid frequency where where

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Resonant Frequencies

ce = ce/2 When B = 5 T and n = 1020 m-3, these frequencies are Mode conversion can change the wave type.

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Electromagnetic Wave Heating

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From H.P. Laqua, Karlsruhe Summer School 2008

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Cavity Resonances

wave wave

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Cavity Resonances

Pass through many times, reflecting from walls. wavelength ~ natural resonance  large amplitude wavelength ~ natural resonance  large amplitude (Like musical instrument) Ch f  h f t f i Changes of n  change of resonant frequencies Generator follows changing resonance (Mode tracking). g g ( g) low impedance  high impedance, improving the coupling efficiency efficiency. Smooth, high-conductivity walls.

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Wave Heating Methods

1 MW

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Wave Heating Methods

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ITER Wave Heating Systems ITER Wave Heating Systems

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From Jean Jacquinot, SOFT 2008

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From Jean Jacquinot, SOFT 2008

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From Jean Jacquinot, SOFT 2008

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Lower Hybrid Wave Propagation Lower Hybrid Wave Propagation

From H.P. Laqua, Karlsruhe Summer School 2008

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ASDEX LH Waveguide Grill

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From H.P. Laqua, Karlsruhe Summer School 2008

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Radiofrequency (rf) Wave Heating

Radiofrequency voltages ~ 30 kV, avoid breakdown Plasma  arcing Rapid shutoff of generators Rapid shutoff of generators Radiation damage to antennas Vacuum windows outside shielding High conductivity after irradiation Waveguide bends

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a egu de be ds

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Summary of Heating, by Heinrich Laqua

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From H.P. Laqua, Karlsruhe Summer School 2008