Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Plasma start-up in tokamaks Winter School - Golem
Document related concepts
Transcript
Plasma start-up in tokamaks Jan Stockel Institute of Plasma Physics, Prague, [email protected] Tokamak plasma has to be "hot". We will talk today on physics of the transition from an empty tokamak vessel to fully ionized, but "cold" plasma. In general, underlying physics is quite complex. We focuse here on selected issues: •Basic hardware/diagnostics to get plasma in a tokamak •Basic physiscs of the start-up phase of a tokamak dischage Any questions during my talk are welcome!! Winter School, Marianska, January 21, 2010 Tokamak basics Tokamak is composed of three basic components • • • Large transformer with primary winding Plasma ring as secondary winding Coils for confinement of plasma ring by magnetic field (toroidal solenoid) Electric current I generated in the plasma ring by the transformer • delivers the ohmic power Pohmic = I2Rplasma to plasma (heating) • generates the poloidal magnetic field in the plasma ring Bpoloidal ~I/2pa However, before ohmic heating, we have to fill the tokamak vessel by fully ionized plasma. This period is called as start-up or breakdown phase of the tokamak discharge. It is a complex process, which begins from well evacuated toroidal vessel. This talk just tackle about basic physics. Sequence of events before a tokamak discharge 1 1. Tokamak is pumped down to to the pressure < 10-4 - 10-3 Pa. 2. Baking of the vessel to 150-2500 and glow discharge cleaning is required! 3. Then, the tokamak vessel is filled by a working gas – but what pressure? 4. At normal conditions (105 Pa, T = 273.15 K) we have n0 = 2,7×1025 m−3 H2 molecules (Loschmit number), i.e. 5.4 ×1025 m−3 atoms is available 5. We require the plasma density ~ 1018 - 1019 m-3 at the breakdown phase. Density of neutral atomic hydrogen should be comparable. 6. Therefore, the initial pressure of H2 should be in the range ~ 0.02 - 0. 2 Pa Sequence of events before a tokamak discharge 2 1. Some free electrons have to be generated inside the vessel by some extermal source (pre-ionization) • electron gun • VUV lamp • cosmic radiation background • eventually RF assisted pre-ionization 2. At least, two power supplies (capacitor banks) to be activated (charged) to drive: * current in the toroidal magnetic field coils Grid Rectifier Capacitor bank Toroidal Field Coils * current in primary winding of the transformer Grid Rectifier Capacitor bank Primary winding of transformer Start-up of a tokamak discharge 1. A trigger pulse is applied to start the data acquisition system Experimental data are collected 2. A trigger pulse is applied to discharge the capacitor bank UBt to toroidal field coils Toroidal magnetic field is generated inside the vessel 3. Wait until a reasonable level of the toroidal magnetic field is reached. (GOLEM – a typical time delay is 1 - 4 ms) 4. A trigger pulse is applied to discharge the capacitor bank Uoh to primary winding of the transformer Time-dependent current in the primary winding generates the toroidal electric field inside the vessel Toroidal electric field – how to measure? Toroidal electric field E tor is required plasma breakdown in tokamaks and for inductive current drive. E tor is generated by transformer (iron- or air-core) by primary current I(t), which has to vary in time. dy/dt – magnetic flux The toroidal electric field is measured by a single loop located along the plasma column: dIprim/dt 0 E tor = Uloop/2pR Loop voltage Uloop = - dy/dt Why the E tor (loop voltage) must be as low as possible during the breakdown? Magnetic flux through the primary windings of a tokamak transformer F(t) = Vloop(t) dt < Fmax Maximum flux Fmax [Weber = Voltseconds] is limited either by quality of the iron core transformer or by mechanical properties of the central solenoid (air-core transformer) CASTOR/GOLEM COMPASS F ~ B*S [Vs] ITER Fmax Fmax = 0.12 Vs (iron core) Fmax = 0.64 Vs – (air-core) (0,4 Vs for breakdown and current ramp-up + 0,24 Vs for flat top phase) Fmax = 277 Vs – (air-core) Iron-core transformer Air-core transformer H ~ Iprim Sequence of events during a discharge Pressure of Hydrogen 50 mPa Toroidal magnetic field Trigger Bt Loop voltage Trigger Uoh Delay Uloop is high enough – Breakdown phase Time Start-up phase of a discharge on CASTOR R plasma = U loop I plasma Te 3 2 Loop voltage [V] Uloop Fully ionized plasma – "hot" (~200 eV) Toroidal current [kA] I_plasma+ I_vessel Fully ionized plasma – "cold" (5-10 eV) Plasma density ne [1018 m-3] 0 I_vessel = I_plasma – Uloop/Rvessel 2 4 Time [ms] 6 Avalanche & Coulomb phases of breakdown Plasma start-up can be divided into two phases with different underlying physics. Therefore, they have to be treated separately. 1. Avalanche phase – degree of ionization is low. Collisions between electrons and hydrogen molecules dominate. Electrons obey a drift velocity vD II Etor, which is higher than their thermal velocity. Plasma current is still low, and the rotational transform is negligible. 2. Coulomb phase – collisions between charged particles dominate. Plasma current is sufficiently high and magnetic surfaces and the confinement is expected to increase significantly. Transition between these two phase occurs when 1 5 10 5 Te 3/ 2 [eV] where is the degree of ionization. Typically, the transition occurs in tokamaks at 5% ionization at Te ~5 eV Electron Fully ionized are plasma fills Density of charged accelerated the vessel (in in 0.1-10 toroidal ms – Free electron(s) particles increases direction depending ionize the size theof appear and inon the vessel exponentially in time working tokamak)gas Avalanche phase of breakdown – ionization length First Townsend coefficient [m-1] = Ap0 exp( Bp 0 / E ITER Lion ~ 2000 m Ionization length Lion [m] Lion = 1 Pressure p0 [Pa] E=Uloop/1pR [V/m] COMPASS For hydrogen (H2) A = 3.75, B = 99 GOLEM Ionization length versus E Drift velocity & Ionization time during the avalanche Electrons obtain a drift velocity vd between ionization collisions, which depends on the ratio of the toroidal electric field and pressure of molecular hydrogen E/p . Only approximation of vd is available for H2: Approx. for 70<E/p<1500 [V/m, Pa] Typically E/p = 80-800 vD = 6,9 104 ( E / p) [m/s, V/m, Pa] Vd ~ 0.55 –2*106 m/s Note: For E/p > 500 , the electron distribution function becomes strongly non-Maxwellian and a significant fraction of electron can run-away! Temporal evolution of plasma density is: n(t ) = n0 exp t ti where the ionization time ti is defined as ti ~ Lion/ vd . Typically, ti ~ 20 ms at p0 ~30 mPa Example: Our final goal is to reach degree of ionization 5%, i.e. the plasma density 5x1017 m-3 with just a single electron inside the tokamak vessel (n0=1 m-3). This occurs during the time interval t = 17 x ln5 x 20 x 10-6 ~ 550 ms !!! HOWEVER – this appears in an ideal case, when all electrons remain inside the vessel during the avalanchel!! Connection length & Loss time during the avalanche REALITY The magnetic field is not strictly toroidal during the start-up. It always has a perpendicular component B, which significantly impacts trajectories of charged particles during the avalanche phase of the discharge. Example B = Bz We can define the connection length Lcon ~ a Btor/ B and an effective loss lime tloss ~ Lcon / vd Rate of the density increase is consequently reduced: 1 1 1 1 t = exp vDt = exp n0 ti tloss Li Lcon and eventually the breakdown may not occur when Lion ~ Lcon n(t ) In practice, the condition Lion ~ 10 x Lcon should be fulfilled Stray magnetic field B from the Toroidal Field coils View from the top , A strong vertical field Bz is created (oriented downwards) Bz = m0I/2pr I = 1 kA, R = 0.4 m Bz(center) ~ 0.15 T !! Installation of Return Current Conductor significantly reduces the Bz field Nevertheless, a small fraction of Bz (<1 mT) could still exists inside the tokamak vessel because of imperfect alignment of TF coils and the return conductor!! Stray magnetic field B from the vessel current Toroidal current through the tokamak vessel (without plasma) generates a vertical magnetic field inside the tokamak vessel Rough estimate (linear approx – lower limit): Bz = m0 I vessel = 10 7 I / R 2pr For 2r = R = 0.8 m and I = 2 kA Bz ~ 0.25 mT For GOLEM a~0.08 m, Btor ~ 0.25 T, B ~ 0.25 mT Lcon ~ 8 m only !! Stray magnetic field from the air-core transformer COMPASS case Strong vertical field is generated, when the primary current flows only through the central solenoid The vertical field is significantly reduced, when the primary current flows also through properly distributed poloidal coils. Evolution of plasma current during the avalanche Plasma current grows exponentially with approx. the same rate as the plasma density during the avalanche phase Iplasma = S*e*ne(t)*vD(t) where S is the cross section of the current channel S=pa2 [m-2] e= 1.6*10-19 C vD(t) =const ~ 106 m/s is the average drift velocity At the end of the avalanche phase, the plasma density is * nmax with the degree of ionization = 0.05 and nmax = 1019 m-3 So, the plasma current at the end of the avalanche phase should be Iplasma (end of avalanche) ~ 8*104 x S [A]. If the current flows through the whole cross section, then: GOLEM COMPASS (S~0.02 m-2) (S~0.12 m-2) TORE Supra (S~1.6 m-2) I ~ 1.6 kA I ~ 9.6 kA I ~ 130 kA Coulomb phase of the start-up Particle balance during the Coulomb phase is described by differential equation for electrons and neutrals dne n = ne n0 Si e dt tp dn0 = ne n0 Si ne dt Si – rate of ionization by electrons tp – particle confinement time – particle influx (recycling) Solution for tp infinity, 0 exp( t / t i ) ne = N N / ne exp( t / t i ) n0 = N ne where N is initial number density of H ti is the ionization time in Coulomb phase ti = 1 NSi Dynamics of atomic/molecular species Dissociation cross section of H2 is greater than the ionization one at low Te Result of modeling including dissociation Te = 6 eV, NH2 ~ 7x 1018 m-3 Ionization rate for atomic hydrogen The ionization rate is a steep function of guessed electron temperatures (3 – 10 eV] Si = v Te = 0,29110 13 U 0,39 exp( U ) [m3/s] 0,232 U where U = 13.6/Te [eV] Approximation for Te < 10 eV: 18 Si = 5,6 10 Te 3 [m3/s, eV] Ionization time at the Coulomb phase for Te = 5 eV and N = 1019 m-3 1 ti = 10 19 1015 = 100ms NSi is longer than during the avalanche Power losses due to collisions with atomic hydrogen Ploss = (ne n0 Si i ) (ne n0 S ex ex ) [W/m 3 ] ionization losses Si Sex = 1,602 1019 [J/eV] excitation losses i = 13,6 eV, ex 10 eV Energy loss per a single ionization/excitation of H0 Ionization and excitation rates are comparable Ploss = 3,776 10 18 ne n0 Si [W/m 3 ] Energy losses are maximum when ne = n0 = N / 2 Ploss MAX Ploss = 9,44 1019 N 2 Si [W/m 3 ] MAX 2 520N19 Te 3 Si = 5,6 1018Te 3 [m3s 1 , eV] N19 = N 1019 [W/m 3 ] N=1*1019 and Te = 6 eV Ploss ~ 200 kW/m3 Power balance at start-up Power losses due to the collisions have to be compensated by ohmic heating res POH = Vloop I p [W/m 3 ] 2p 2 Ra 2 CAST0R- Ohmic power during start up: Volume 0.1 m3, Vloop~ 10 V, Ip ~ 2 kA Poh ~ 200 kW/m-3 The electron temperature can be roughly estimated from the power balance POH Ploss MAX 2 520N19 Te POH Te 2 520 N19 1 3 [W/m3 ] 3 [eV, W/m 3 ] CASTOR N= 1019 m-3 and POH~200 kW/m-3 Te ~ 7.2 eV This number is an upper limit for Te – some fraction of POH is consumed to heat electrons Conclusions I tried to explain some underlying physics of the plasma start-up in tokamaks. • Two phases were defined * Avalanche phase * Coulomb phase • We focus on the avalanche phase • importance of ionization and connection lengths (stray magnetic fields) Many relevant features were not discussed at all (role of impurities, RF assisted pre-ionization, runaway electrons, plasma current ramp-up, …..) More information is available in many publications upon request at [email protected] Thanks for attention those who did not sleep, but also to sleepers, who did not snore!!
