1. Particle acceleration and plasma heating in the chromosphere Alexander Stepanov, Pulkovo Observatory, St.Petersburg, Russia Valery Zaitsev Institute of Applied Physics, N.Novgorod, Russia Prague “Solar and stellar Flares” June 23-27, 2014

2. OUTLINE OF TALK BBSO New Solar Telescope : in situ choromosphere heating Rayleigh-Taylor instability: General Particle acceleration mechanism by induced electric field Chromosphere heating mechanism (collisions) Consequences: Plasma radiation at sub-THz from chromosphere Origin of sub-THz pulsations: Electric circuit model Electric current diagnostics Deja vu – come back to the ‘chromospheric flare’.

3. Haisheng Ji et al. (ApJ Lett 2012): In situ chromosphere heating to T ≥ 10 6 K. Observation of Ultrafine Channels of Solar Corona Heating Haisheng Ji et al. 2012 ApJ 750 L25 Indications on chromosphere heating in situ Sharykin & Kosovitchev (ApJ 2014): BBSO observations reveal previously unresolved sub-arcsecond structure of the flare ribbons consisting from numerous small-scale (≤ 100 km) bright knots. Plasma is heated to high temperature by some another mechanism different from thick-target model. I ≈ 5×10 10 A. Joule heating?

4. Rayleigh-Taylor instability (Carlyne et al. ApJ 2014)

5. Rayleigh-Taylor Instability (Ballooning mode) in Corona and Chromosphere Prominence at the loop top Fp=ρgFp=ρg F c = 2nTR c /R c 2 Instability condition:

6. Ballooning Instability in a Current-carrying Magnetic Loop To determine the temperature to which the chromosphere should be heated we used a modified Saha formula: for Current dissipation is provided by the Cowling conductivity related to electron-atom collisions. The radiation losses From q j > q r we obtain the lower boundary for the rate of photosphere convection that provides pre-heating:

7. Induced electric field in a current-carrying loop Before R-T Instability: Penetration of chromosphere plasma into a loop with velocity From Eqs and No acceleration!. But for the time s a disturbance dealing with is running away from instability domain as a non-linear Alfven wave: E || B z appears and particle acceleration is realized in the electric field for E ≈ 0.1 V/cm and the electron energy is about Є ≈ 1 MeV.

8. Particle Acceleration & Chromosphere Plasma Heating Disturbance of electric current in flare loop due to ballooning instability. Electric field generation. Electron acceleration by induced Е-field. Heating of chromosphere plasma by accelerated electrons. Accelerated particles don’t leave the source and lost energy completely. Plasma heating rate by fast particles (Knopfel & Spong, 1979): Radiation losses q r < q s for E D /E z ≈ 40, E D is Dreicer field. Particle mean free path:

9. FLARING LOOP Ballooning instability THz- source “Transparency” conditions for chromosphere: - Large currents in flaring loops ~10 11 A - Ballooning instability, which induced electron acceleration in the chromosphere, plasma heating and plasma wave turbulence generation. Even for В = 2000 G ω p / ω сe ≈ 40 >>1. So, isotropic plasma approximation is true. Requirements to the source: Consequences: Plasma radiation in sub-THz (Sakai et al. 2006; Zaitsev, Stepanov, Melnikov, 2013)

10. Conversion l→ t : Radiation at the fundamental ( ω = ω p ) and harmonic ω = 2ω p = (4 π )×200 GHz T b2 ~ (nT)w 2 w = W p l/nT “Transparency” at plasma turbulence level w ≥ 10 -4 Maser-effect μ < 0: Solar plasma radiation: at sub-THz at MHz-GHz

11. Challenge in solar physics: > 10 4 sfu emission at 212 and 405 GHz with pulsations (Kaufmann et al. 2004, 2009). Pulsations with modulation depth 5-8% and periods 0.2-4 s. Consequences: Pulsations at sub-THz from solar flares (Zaitsev, Stepanov, Kaufmann, SP 2013) Puzzling proportionality between pulse repetition rate and mean emission fluxes

12. We suggest electric circuit model (RLC) for QPPs Modified Alfven oscillations: ν RLC = V Aφ /r – that is RLC-pulsations with к almost perpendicular to В (cosθ = Bφ/Bz << 1). Flare trigger: – plasma tongue driven by ballooning instability Current in the flare I ≈ 10 11 A. Let us determine L, C, R и Q: L ≈ 10l = 10 10 сm = 10 Henry; С = (с 2 /V A 2 )S/l ≈ 10 11 сv = 0.1 F. Period Р = √LC ≈ 1 с. Q-factor Q = R -1 (L/C) 1/2 R eff = W/I 2 = 10 18 W/10 22 А 2 = 10 -4 Ohm e.i. Q ≈ 3×10 4 >> 1

13. Coronal loop as an equivalent RLC-circuit For small current deviation → the equation of a linear oscillator (Khodachenko et al 2009): Excitation: Oscillation frequency Quality factor

14. Diagnostic of electric current in a flare using pulsations at sub-THz From pulse rate variation in the flare on 4 November 2003 (Kaufmann et al. ApJ, 2009) a decrease of the electric current from 1.7×10 12 А in the flare maximum to 4×10 10 А after the burst was found.

15. Conclusions Rayleigh-Taylor instability plays important role in particle acceleration and plasma heating in deep layers of the solar atmosphere. Deja vu – back to the ‘chromospheric flare’ (Ŝvestka, Fritsova- Ŝvestkova) Coronal flares ate also possible To comprehend physics of solar chomosphere flares more multi-wavelength observations including THz band are needed.

16. Thank you