How to lock or limit a free ballistic expansion of energetic particles
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How to lock or limit a free ballistic expansion of Energetic Particles?. What could limit the free collisionless expansion?. Dominant Scenario: -Instabilities / to create the “waves (as scatterers)”; -Feedback of growing fluctuations on particles due to the particles – waves interaction;

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What could limit the free collisionless expansion

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;



Implementation of such scenario
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


V Particles?

ADD MORE WAVES

X


Width of resonance Particles?

vs.

Distance between

resonances


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
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
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.






Net effect of instabilities
Net effect of Instabilities Current

  • Both types of Instability together:


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