DSA in the non-linear regimeHui LiDepartment of Astronomy, Nanjing University

Test-Particle approximationBell 1978

Relationship!ThermalparticlesCRsAlfven waveDSAHeating, ionizing; Back PressureStreaming instabilitiesConfine and promote accHeating and pre-heatingMHD turbulence and instabilitiesISM

Non-linear effects: IShock structure: precursor and CD; RTTemperatureConcaved CR spectrum

Non-linear effects: IIMFA produced by CRs streaming instability. CR energywave energy

Numerical treatmentsTwo-fluid model. (Drury&Voelk 1981 a,b)Kinetic theory: a. fully numerical simulation (Berezhko & Voelk 1997; Kang & Jones 1997, 2005, 2006, 2007; Zirakashvili & Aharonian 2010) b. Monte Carlo simulation (Ellison & Eichler 1984,1985; Vladimirov et al. 2006) c. quasi-stationary semi-analytical solution (Blasi et al. 2007; Caprioli et al 2009)

Two-fluid ModelTreat the accelerated particles as a second fluid with energy density E_c and pressure P_c, but negligible mass density.Drury & Voelk 1981

Two-fluid ModelUseful to study the dynamics of a shock modified by the presence of acc CRs.Cant provide any information about the spectrum of energetic particles.

Fully numerical simulationForward shock injectionReverse shock injectionKang & Jones 2006Zirakashvili & Aharonian 2010

Fully numerical simulation1-DHD instabilities ignoredCant use mature MHD codes.Zirakashvili & Aharonian 2010

Semi-analytical solutionGuess solution:static-state solutionIterate until stable!!Blasi 2002; 2004; 2005; Caprioli et al. 2010

ComparisonCaprioli et al. 2010

A new way??HD simulation+CR modificationInstabilities?Inhomogenous environments? Warren et al. 2005

How to deal with CR feedback?HD simulation output: a. shock information: V_s, M_s. b. injection recipe: c. cutoff recipe: p_maxSemi-analytical approximation: _eff= _eff(V_s,M_s,p_inj,p_max)Re-input _eff into the HD simulation

Blondin & Ellison 20011-D2-DGrowth of instab. suppressed by CR acc

3-D?Ferrand et al. 2009Pure HD caseWith back reactionInstability level?

Where are we now? ObservationalShock Dynamic?Shock structure: precursor and CDHelder et al. 2009;Warren et al. 2010RCW86SN1006Tycho

Lower temperature?Concaved CR spectrumSN 1006J1713Berezhko et al 2002; 2009Ellison et al. 2010

MFA?Thin filaments in X-ray? Time scale? X-ray knots?The extreme cooling or fast variation of MF?Why radio filaments?Time scale of instability?Which instability dominates?

Where are we now? TheoreticalKnow little about DSA!!Self-consistent ways of injections of super-thermal particles? Thermal leakage?Self-consistent ways of escaping of relativistic CRs? Maximum energy and free escaping boundary?Self-consistent ways of wave excitation and magnetic field amplification?

PIC may help, but .

What can we do?HD Simulation? CR influence on instability; SNR-MC; MHD simulation; MFA? Filament width vs. shock velocity?Observational constrain on non-linear filaments micro-structure; cut-off energy; line emission on lower temperature; ion temperature?

Thank you!