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How to lock or limit a free ballistic expansion of Energetic Particles?PowerPoint Presentation

How to lock or limit a free ballistic expansion of Energetic Particles?

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## PowerPoint Slideshow about ' How to lock or limit a free ballistic expansion of Energetic Particles?' - ishmael-hopkins

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### What could limit the free collisionless expansion? Particles?

Dominant Scenario:

-Instabilities / to create the “waves

(as scatterers)”;

-Feedback of growing fluctuations on particles due to the particles – waves interaction;

-Non-Linear saturation of instability / build up of saturation spectrum;

Add Fermi Acceleration Particles?

Implementation of such scenario Particles?

- -Instability: Velocity Anisotropy (“Cyclotron Instability” of Alfven waves);
- -Feedback on particles: Quasilinear Theory of Particles/Cyclotron Waves Interaction;
- -Non-Linear saturation: Strong MHD / Alfven Waves/ Turbulence;

Connection of Quasilinear Theory to KAM-Theory: Particles?

From Planetary Resonances to Plasma

V Particles?

x

much less than Particles?

This limit corresponds to KAM (Kolmogoroff-Arnold-Mozer) case.

KAM-Theorem :

As applied to our case of Charged Particle – Wave Packet Interaction –

“Particle preserves its orbit “

greater than Particles?

That means - overlapping of neighboring resonances

Repercussions:

-”collectivization” of particles between neighboring waves;

-particles moving from one resonance to another – “random walk”? And if yes

-what isDiffusion Coefficient ?(in velocity space)

V Particles?XdV/dt =

D= Particles?

Repercussions: Quasilinear Theory, Plateau Formation,

Beam + Plasma Instability Saturation etc.

General Conclusions Particles?

- Kolmogoroff: Application of KAM theory to the Dynamics of Planetary System
- Plasma case: Application to the Dynamics of Charged Particles
more applications:

- Waves-Particles interaction at Cyclotron Resonance
- Magnetic Surfaces Splitting? (Trieste, 1966)
- Advection in Fluids (+20 years)

Quasilinear Diffusion Particles?

- . The simplified approach to such diffusion is equivalent to a truncation of quasilinear velocity space diffusion similar to tau-approximation form of collision integral in kinetic equation .
Further simplifications:

- -Plasma pressure is much greater than Magnetic field pressure;
- -Bulk of plasma particles out of resonance with “waves” (even in strong turbulence definition);
- -CR particle density too small to produce competitive nonlinear effects by themselves and do not affect waves nonlinear saturation process.

Add Fermi Acceleration Particles?

Truncate Quasilinear Eqn Particles?

Nonlinear Saturation Conjecture Particles?

MHD + Expanding Cloud of Energetic Particles + “Return Current

MHD Waves modified:

Net effect of Instabilities Current

- Both types of Instability together:

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