Scattering length of relativistic particles in aperiodic - PowerPoint PPT Presentation

Scattering length of relativistic particles in aperiodic fluctuations Scattering length Motivation Particle/Field Anne Stockem The Filamentation Instability Ruhr-University Bochum, Theoretical Space and Astrophysics Conclusions October 2008 RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Scattering length Motivation Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Scattering AF: Magnetic field length generation Motivation Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions Reduction of instabilities RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions Reduction of instabilities Scattering length: Condition: Instability RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions Reduction of instabilities Scattering length: Condition: Instability Interaction: Particles/Field RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions Reduction of instabilities Scattering length: Condition: Instability Interaction: Particles/Field Inside the system?! RUB, TPIV Anne Stockem Scattering length

Outline Motivation: Solar eruption: Scattering AF: Magnetic field length generation Motivation Origin of magnetic fields Particle/Field The Many applications in Filamentation Instability Space and Astrophysics Conclusions Reduction of instabilities Scattering length: Condition: Instability Interaction: Particles/Field Inside the system?! Scattering length RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Motivation Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Lorentz force F L = q v × B Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Lorentz force F L = q v × B Filamentation Instability Charge separation Conclusions RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Lorentz force F L = q v × B Filamentation Instability Charge separation Conclusions Right hand rule: amplification of B y RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Lorentz force F L = q v × B Filamentation Instability Charge separation Conclusions Right hand rule: amplification of B y Non-linear phase: Biot-Savart interaction RUB, TPIV Anne Stockem Scattering length

The Physical Principle Linear phase: Scattering Counterstreaming particles length Magnetic field fluctuation Motivation δB y ( x, t ) = B y ( t ) e ıkx Particle/Field The Lorentz force F L = q v × B Filamentation Instability Charge separation Conclusions Right hand rule: amplification of B y Non-linear phase: Biot-Savart interaction Merging of the current filaments RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: Scattering length Motivation Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Motivation Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Conclusions RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L Interaction inside the system RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L Interaction inside the system Instability possible RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L Interaction inside the system Instability possible Consequences: RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L Interaction inside the system Instability possible Consequences: Calculation of λ RUB, TPIV Anne Stockem Scattering length

Interaction between Particles and Field 1. Case: No interaction: Scattering λ �≪ L length Particle leaves the system Motivation before being scattered Particle/Field The No instability Filamentation Instability 2. Case: Interaction: Conclusions λ ≪ L Interaction inside the system Instability possible Consequences: Calculation of λ Appropriate model is necessary! RUB, TPIV Anne Stockem Scattering length

The Scattering Length Parallel mean free path length: Scattering � 1 dµ (1 − µ 2 ) 2 length λ � = 3 v 8 D µµ ( µ ) Motivation − 1 Particle/Field Jokipii (1966); Hasselmann and Wibberenz (1968); Earl (1974) The Filamentation Instability Conclusions RUB, TPIV Anne Stockem Scattering length

The Scattering Length Parallel mean free path length: Scattering � 1 dµ (1 − µ 2 ) 2 length λ � = 3 v 8 D µµ ( µ ) Motivation − 1 Particle/Field Jokipii (1966); Hasselmann and Wibberenz (1968); Earl (1974) The Filamentation Instability Diffusion coefficient: Conclusions � ∞ � ∞ ds e Γ( k ⊥ ) s f ( k ⊥ , µ, s ) D µµ ( µ ) = const. dk ⊥ 0 k min RUB, TPIV Anne Stockem Scattering length