1. Plasma start-up in tokamaks Winter School, Marianska, January 21, 2010 Jan Stockel Institute of Plasma Physics, Prague, stockel@ipp.cas.cz 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!!

2. 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 P ohmic = I 2 R plasma to plasma (heating) generates the poloidal magnetic field in the plasma ring B poloidal ~I/2  a 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.

3. 1.Tokamak is pumped down to to the pressure < 10 -4 - 10 -3 Pa. 2.Baking of the vessel to 150-250 0 and glow discharge cleaning is required! 3.Then, the tokamak vessel is filled by a working gas – but what pressure? 4.At normal conditions (10 5 Pa, T = 273.15 K) we have n 0 = 2,7×10 25 m −3 H 2 molecules (Loschmit number), i.e. 5.4 ×10 25 m −3 atoms is available 5.We require the plasma density ~ 10 18 - 10 19 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 1

4. 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 * current in primary winding of the transformer Sequence of events before a tokamak discharge 2 Capacitor bank Toroidal Field Coils Grid Rectifier Capacitor bank Primary winding of transformer GridRectifier

5. 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 U Bt 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 U oh to primary winding of the transformer  Time-dependent current in the primary winding generates the toroidal electric field inside the vessel Start-up of a tokamak discharge

6. 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. Toroidal electric field – how to measure? d  /dt – magnetic flux Loop voltage U loop = - d  /dt The toroidal electric field is measured by a single loop located along the plasma column: E tor = U loop /2  R dIprim/dt  0

7. 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  t  Vloop(t) dt <  max Maximum flux  max [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  max = 0.12 Vs (iron core) COMPASS  max = 0.64 Vs – (air-core) (0,4 Vs for breakdown and current ramp-up + 0,24 Vs for flat top phase) ITER  max = 277 Vs – (air-core) Iron-core transformer Air-core transformer H ~ I prim  B*S [Vs]  max

8. Sequence of events during a discharge Toroidal magnetic field Pressure of Hydrogen Loop voltage U loop is high enough – Breakdown phase 50 mPa Time Delay Trigger BtTrigger Uoh

9. Loop voltage [V] Uloop Toroidal current [kA] I_plasma+ I_vessel Plasma density n e [10 18 m -3 ] Start-up phase of a discharge on CASTOR Time [ms] 02 4 6 I_vessel = I_plasma – Uloop/Rvessel Fully ionized plasma – "cold" (5-10 eV) Fully ionized plasma – "hot" (~200 eV)

10. 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 v D II E tor, 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 Avalanche & Coulomb phases of breakdown where  is the degree of ionization. Typically, the transition occurs in tokamaks at 5% ionization at Te ~5 eV [eV]

11. Electron are accelerated in toroidal direction and ionize the working gas Fully ionized plasma fills the vessel (in 0.1-10 ms – depending on the size of tokamak) Density of charged particles increases exponentially in time Free electron(s) appear in the vessel

12. Avalanche phase of breakdown – ionization length First Townsend coefficient  [m-1] Pressure p 0 [Pa] E=U loop /1  R [V/m] For hydrogen (H2)  A = 3.75, B = 99 Ionization length L ion  [m] Ionization length versus E GOLEM COMPASS ITER L ion ~ 2000 m

13. Drift velocity & Ionization time during the avalanche [m/s, V/m, Pa] Approx. for 70<E/p<1500 [V/m, Pa] Typically E/p = 80-800 V d ~ 0.55 –2*10 6 m/s Electrons obtain a drift velocity v d between ionization collisions, which depends on the ratio of the toroidal electric field and pressure of molecular hydrogen E/p. Only approximation of v d is available for H 2 : 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: where the ionization time t i is defined as t i ~ L ion / v d. Typically, t i ~ 20  s at p 0 ~30 mPa Example: Our final goal is to reach degree of ionization 5%, i.e. the plasma density 5x10 17 m -3 with just a single electron inside the tokamak vessel (n 0 =1 m -3 ). This occurs during the time interval t = 17 x ln5 x 20 x 10 -6 ~ 550  s !!! HOWEVER – this appears in an ideal case, when all electrons remain inside the vessel during the avalanchel!!

14. Connection length & Loss time during the avalanche Example B  = Bz We can define the connection length L con ~ a B tor / B  and an effective loss lime  loss ~ L con / v d Rate of the density increase is consequently reduced: and eventually the breakdown may not occur when L ion ~ L con In practice, the condition L ion ~ 10 x L con should be fulfilled 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.

15. Stray magnetic field B  from the Toroidal Field coils View from the top A strong vertical field B z is created (oriented downwards) 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!!, B z =  0 I/2  r I = 1 kA, R = 0.4 m B z (center) ~ 0.15 T !!

16. 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): For 2r = R = 0.8 m and I = 2 kA  B z ~ 0.25 mT For GOLEM a~0.08 m, Btor ~ 0.25 T, B  ~ 0.25 mT  L con ~ 8 m only !!

17. Stray magnetic field from the air-core transformer 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. COMPASS case

18. Evolution of plasma current during the avalanche Plasma current grows exponentially with approx. the same rate as the plasma density during the avalanche phase I plasma = S*e*n e (t)*v D (t)where S is the cross section of the current channel S=  a 2 [m-2] e= 1.6*10 -19 C v D (t) =const ~ 10 6 m/s is the average drift velocity At the end of the avalanche phase, the plasma density is  * n max with the degree of ionization  = 0.05 and n max = 10 19 m -3 So, the plasma current at the end of the avalanche phase should be I plasma (end of avalanche) ~ 8*10 4 x S [A]. If the current flows through the whole cross section, then: GOLEM (S~0.02 m-2) I ~ 1.6 kA COMPASS (S~0.12 m-2) I ~ 9.6 kA TORE Supra (S~1.6 m-2) I ~ 130 kA

19. Coulomb phase of the start-up Particle balance during the Coulomb phase is described by differential equation for electrons and neutrals S i – rate of ionization by electrons  p – particle confinement time  – particle influx (recycling) Solution for  p  infinity,  0 where N is initial number density of H  i is the ionization time in Coulomb phase

20. 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, N H2 ~ 7x 10 18 m-3

21. Ionization rate for atomic hydrogen The ionization rate is a steep function of guessed electron temperatures (3 – 10 eV] [m 3 /s] where U = 13.6/Te [eV] [m 3 /s, eV] Approximation for Te < 10 eV: Ionization time at the Coulomb phase for Te = 5 eV and N = 10 19 m -3 is longer than during the avalanche

22. Power losses due to collisions with atomic hydrogen ionization lossesexcitation losses Ionization and excitation rates are comparable Energy loss per a single ionization/excitation of H 0 Energy losses are maximum when N=1*10 19 and Te = 6 eV P loss ~ 200 kW/m 3

23. Power balance at start-up Power losses due to the collisions have to be compensated by ohmic heating CAST0R- Ohmic power during start up: Volume 0.1 m 3, V loop ~ 10 V, I p ~ 2 kA  P oh ~ 200 kW/m -3 The electron temperature can be roughly estimated from the power balance CASTOR N= 10 19 m -3 and P OH ~200 kW/m -3  Te ~ 7.2 eV This number is an upper limit for Te – some fraction of P OH is consumed to heat electrons

24. 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 stockel@ipp.cas.cz Thanks for attention those who did not sleep, but also to sleepers, who did not snore!!

25. Ohmic heating power at the start-up phase where Let us take the loop voltage V loop and the major radius R as known quantities. Moreover, the loop voltage is almost the same for all tokamaks! (we neglect inductive losses)

26. Power balance at start-up