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hi ,, hello dears
first i hope i choose the suitable section to put my question

i want in fact to distinguish between different methods to model or study or describe plasma physics .. from my read i found that there are various ways to study plasma physics one way is the single particle description which held by following the trajectory of each particle but this is very complicated method due to large number of particles ,, other models is the kinetic model and fluid model in fact here my confusion appeared i cant distinguish between them what is the major difference between them and why the fluid model is more simpler .. i hope my question is specific and clear :)

I think the part you might be confused about is, while the particle model is *conceptually* simple since each particle is rather simple, it's the ability to make predictions that is super-hard. How do you calculate the behavior of 1023 particles?
The fluid model takes a high-level approach, thus being mathematically much more tractable.

I think the part you might be confused about is, while the particle model is *conceptually* simple since each particle is rather simple, it's the ability to make predictions that is super-hard. How do you calculate the behavior of 1023 particles?
The fluid model takes a high-level approach, thus being mathematically much more tractable.
mm i understood the difficulty at dealing with such high number of particles
could i say that both kinetic and fluid model are both statistical approaches or what in fact the difference between both of them

Khashishi
I think you have the right idea. Kinetic and fluid models are a sort of coarse-grained model. Both of them treat the plasma as a continuous medium, when in fact it is made up of a large number of particles. This allows us to ask questions like, what is the density of the plasma at a point (x,y,z). The plasma parameters are averaged over a small volume around the point. The number of particles is generally so large that we aren't too concerned about each individual one.

The difference between kinetic and fluid models is that a kinetic model is more complete and contains information about the full distribution functions of the particles involved, while fluid models only contains information about the (statistical) moments of the distribution functions. A distribution function tells you how many particles have a particular velocity near a point in space. The zeroth, first, and second moments of this distribution function give you the total number of particles near this point in space (the density), the average velocity, and the temperature.

So, with a fluid model, we can say the fluid is moving with velocity (vx, vy, vz) at point (x, y, z). But that doesn't mean every particle is moving at velocity (vx, vy, vz). If the particles have a Gaussian distribution of velocities (MB distribution of speeds), then a fluid model will probably work fine, since the entire distribution function can be described by just the amplitude, center, and width of the Gaussian, which correspond to the density, velocity, and temperature of the fluid. But if the distribution function has a weird shape which can't be described by a few moments, then the fluid model will be inadequate.

I think you have the right idea. Kinetic and fluid models are a sort of coarse-grained model. Both of them treat the plasma as a continuous medium, when in fact it is made up of a large number of particles. This allows us to ask questions like, what is the density of the plasma at a point (x,y,z). The plasma parameters are averaged over a small volume around the point. The number of particles is generally so large that we aren't too concerned about each individual one.

The difference between kinetic and fluid models is that a kinetic model is more complete and contains information about the full distribution functions of the particles involved, while fluid models only contains information about the (statistical) moments of the distribution functions. A distribution function tells you how many particles have a particular velocity near a point in space. The zeroth, first, and second moments of this distribution function give you the total number of particles near this point in space (the density), the average velocity, and the temperature.

So, with a fluid model, we can say the fluid is moving with velocity (vx, vy, vz) at point (x, y, z). But that doesn't mean every particle is moving at velocity (vx, vy, vz). If the particles have a Gaussian distribution of velocities (MB distribution of speeds), then a fluid model will probably work fine, since the entire distribution function can be described by just the amplitude, center, and width of the Gaussian, which correspond to the density, velocity, and temperature of the fluid. But if the distribution function has a weird shape which can't be described by a few moments, then the fluid model will be inadequate.

so happy that finally one put his hand on my confusion
at first i apologize as i am a beginner at his topic so my question may appear trivial

you said ' with a fluid model, we can say the fluid is moving with velocity (vx, vy, vz) at point (x, y, z). But that doesn't mean every particle is moving at velocity (vx, vy, vz)' your sentence agree with what i read at books but from my ideas isn't fluid treated a whole as if it has only one average velocity ?? to be more clear if i treat the fluid such water then all species of the following water will move together with average velocity ??

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Khashishi