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

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’.

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 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?

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

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:

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:

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.

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:

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)

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 ≥ Maser-effect μ < 0: Solar plasma radiation: at sub-THz at MHz-GHz

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 s. Consequences: Pulsations at sub-THz from solar flares (Zaitsev, Stepanov, Kaufmann, SP 2013) Puzzling proportionality between pulse repetition rate and mean emission fluxes

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 ≈ A. Let us determine L, C, R и Q: L ≈ 10l = сm = 10 Henry; С = (с 2 /V A 2 )S/l ≈ сv = 0.1 F. Period Р = √LC ≈ 1 с. Q-factor Q = R -1 (L/C) 1/2 R eff = W/I 2 = W/10 22 А 2 = Ohm e.i. Q ≈ 3×10 4 >> 1

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

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.

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.

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