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

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 dolan swip 2009 1

ITER Heating Methods g microwaves dolan swip 2009 2

Plasma Heating Methods Ohmic Ohmic – current flow through plasma. 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 = 10 20 m -3 T = 10 keV V = 200 m 3 Example: n = 10 20 m 3 , T = 10 keV, V = 200 m 3 . W = 1.5n(T e +T i ) ≈ 100 MJ. Maybe 50 MW for about 10 s. dolan swip 2009 3

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. o cost pe att dolan swip 2009 4

Ohmic Heating Electrodes or magnetic induction can drive plasma current. Power dissipated per m 3 is For Zeff = 1 and L = 18 For Zeff = 1 and L = 18, Resistivity of copper at room temperature is about 2x10 -8  -m. dolan swip 2009 5

Increases of Resistivity  Neutral atoms increase  by factor Neutral atoms increase  by factor Impurity ions increase Zeff and  Toroidal geometry Trapped particles  eff >>  ei  >>  Turbulence Turbulence 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, but auxiliary heating is usually needed. dolan swip 2009 6

Runaway Electrons m e ( ∂ u e / ∂ t) = -eE װ +  װ J װ - m e u e  en If |eE װ | > |  װ J װ – m e u e  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. dolan swip 2009 7

Compression dolan swip 2009 8

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. dolan swip 2009 9

Shock Waves in Gases Rupturing diaphragm between gases at different pressues 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). dolan swip 2009 10

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) dolan swip 2009 11

Shock Wave Heating Shock Wave Heating P Problems bl Low inductance, high voltage. , g g Neutrons damage coils and insulators . Fatigue failures, limit coil B field. dolan swip 2009 12

Adiabatic Compression N = number of degrees of freedom during compression. 1D compression   = 3; 2D   = 2; 3D   = 5/3. 1D i  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. e and T i , then  = 5/3. If collisions equalize T dolan swip 2009 13

Compression of Toroidal Plasma C Compressed along d l Initial plasma Minor radius C Compressed along d l Major radius dolan swip 2009 14

Compression of Toroidal Plasma Compute Volume Change: low beta plasma low-beta plasma high beta plasma high-beta plasma Then compute change of W i dolan swip 2009 15

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. dolan swip 2009 16

P Partice Injection i I j i dolan swip 2009 17

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. dolan swip 2009 18

Plasma Guns Injected into a tokamak: Charge-separation E field Charge separation E field helps plasma to penetrate across B . “ Plasma focus ” is collapse of plasma blob to small diameter. Used as source of x-rays or neutrons. Vortex filaments observed. dolan swip 2009 19

RACE Device Livermore RACE Device, Livermore Plasma ring accelerator 0.1 mg plasma rings 40 kJ 20% efficiency 20% efficiency v = 10 6 m/s dolan swip 2009 20

Tokamak de Varennes Canada Tokamak de Varennes, Canada Plasma gun v ~ 2x10 5 m/s Pl 2 10 5 / dolan swip 2009 21

Neutral Beam Injection (NBI) Energy too low Energy satisfactory r Energy too high Energy too high dolan swip 2009 22

Neutral Beam Injection (NBI) Unattenuated beam density  a = attenuation length. In a uniform plasma From graph, D at 100 keV n e  a = 3x10 19 m -2 . If n = 10 20 m -3 then If n e = 10 20 m -3 , then  a = 0.3 m. T e = 10 keV (smooth curve) T T e = 1 keV (dashed curve) 1 keV (dashed curve) e dolan swip 2009 23

NBI Penetration ~ a/4 a NBI a/4 r dolan swip 2009 24

Neutral Beam Injection (NBI) Let  av =  evaluated at <n e > and <T e >.  av > a/4 may give adequate penetration. Example: n e = 8x10 19 m -3 , a = 1.0 m. n e a = 8x10 19 m -2 . Require n e  av > 2x10 19 m -2 . q e av Required W o ≈ 70 keV. dolan swip 2009 25

26 Neutral Beam Production dolan swip 2009

DuoPIGatron Ion Source 22 cm diameter 22 di t A = anode Penning discharge F = filaments B B z M = magnet coils e - e - -        -     dolan swip 2009 27

LBL Ion Source LBL i LBL ion source uses B = 0, higher arc current. p ~ 1 Pa. 0 hi h t 1 P B 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 + (1/2 energy per atom) 20% D 2 t ) + (1/3 energy per atom) 10%D 3 TFTR extraction area 10x40 cm 120 keV, 65 A per source. dolan swip 2009 28

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, to allow thermal expansion. J ~ 3 kA/m 2 attained. If sparking occurs, high voltage must be switched off immediately. decelerating dece e at g Accelerating Accelerating grid grid dolan swip 2009 29

TFTR Neutral Beam Injector 0.2 T Magnetic field shielded by steel to avoid damaging plasma confinement. 5 x 7 m dolan swip 2009 30

Neutral Beam Injection (NBI) F Fraction of ion beam neutralized by charge exchange ti f i b t li d b h h  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. dolan swip 2009 31

TFR Neutral Beam Injection (NBI) P Per MW of D o MW f D o Four units  20 MW (D o ) Pulse length = 0.5 s dolan swip 2009 32

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 P o tL d /C. P o = 5 MW, t = 0.5 s, L d = 2.5 m, C = 150 m 3 /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%. dolan swip 2009 33

NBI Design Considerations Current density – maximize J, high  , narrow gaps J hi h  C t d it i i 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 close to accelerating grids l t l ti id Overheating – cooling by water, helium, or liquid metal. g g y q Arc damage – computerized diagnostics, fast circuit- interrupters on power supplies interrupters on power supplies. dolan swip 2009 34