Physics of fusion power. Collisions / Transport (Lecture 14)

Сентябрь 15, 2022

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Physics of fusion power. Collisions / Transport (Lecture 14)

Содержание

2. Collisions Coulomb interaction between electrons and ions leads to the scattering of particles -> Collisions Interaction
3. Small / Large angle scattering Deflection depends on how close the particles approach each other For
4. Many body problem The plasma has some 1022 particles. No description is possible that allows for
5. Diffusion of the velocity direction
6. Diffusion of the velocity Diffusion coefficient Define a function that determines the number of particles moving
7. Transport in a homogeneous magnetic field Particles undergo scattering. The diffusion coefficient Typical step size is
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Collisions
Coulomb interaction between electrons and ions leads to the scattering

of particles -> Collisions
Interaction occurs only within the Debye sphere
The angle of deflection depends on how close the particles are approaching each other.

Collisions between the ions

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Small / Large angle scattering
Deflection depends on how close the

particles approach each other
For a given time a particle moving through the plasma will collide with all particles in a cylinder
For large angle scattering collisions the distance must be small and so is the radius of the cylinder
For small angle scattering collisions the radius is much larger
It turns out that small angle scattering collisions dominate

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Many body problem
The plasma has some 1022 particles. No description

is possible that allows for the determination of position and velocity of all these particles
Only averaged quantities can be described.
The evolution of the averaged velocity is however influenced by a microscopic process : the collisions
Each collision can have a different outcome depending on the unknown initial conditions

Depending on the (unknown) initial conditions the outcome of a collision can be very different

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Diffusion of the velocity direction

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Diffusion of the velocity
Diffusion coefficient
Define a function that determines

the number of particles moving in a direction given by the angle θ
Collisions lead to a diffusion in the angle described by

Initial distribution of particles moving mostly in the same direction (same angle) are scattered by collisions which randomize the angle of propagation

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