Arbitray initial plasma profile as input

[cjoycd]

Dear developers,

I would like to initiate a simulation with a spatially varying plasma density. In this case, the ion charge state (Z*) will also vary spatially for a given species. I can specify variations in the ion number density as well as the electron number density using input decks. However, I am finding it difficult to incorporate spatial variations in the ion charge state.

Is there a way to set the charge state as the ratio of electron to ion number density, or can this be specified (loaded) directly via an input file? It would be helpful if a sample input deck or an example of particle loading using an input file could be provided. Any guidance on this would be greatly appreciated.

Thank you in advance.
--Sijoy CD

[TomGoffrey]

You can't specify charge state directly, you'd have to specify each ion species individually.

The simplest example would be for a hydrogen plasma, where you could do something like:

begin:constant
   n_0 = 1e28
   zstar = n_0 * exp(-x)
end:constant

begin:species
   name = Electron
   charge = -1.0
   mass = 1.0
   number_density = zstar
   ...
end:species

begin:species
   name = H1
   charge = 1.0
   mass = 1836.0
   number_density = number_density(Electron)
   ...
end:species

begin:species
   name = H0
   charge = 0.0
   mass = 1836.0
   number_density = n_0 - number_density(H1)
   ...

This would give you an exponentially decaying charge state as a function of x. For higher Z materials it becomes more complex, and less well specified - a given charge state could have multiple combinations of ionisation states. Is there a specific profile you're thinking of?

[cjoycd]

Dear Tom Goffrey,

Thank you for your reply.

I am trying to incorporate pre-plasma conditions generated using a separate continuum calculations into PIC, this pre-plasma conditions are the initial conditions for the PIC simulations. Here, I have a spatially varying electron plasma number density (ne(x)) with spatially varying ion number density (ni(x)) and charge state (Z(x)) . I have a consistent profile such that ne(x) = Z(x) * ni(x) satisfying quasi-neutrality. I can easily give the profile for both ions and electrons independently with a charge state say Z at all spatial locations (constant). This however, deviates from my actual initial conditions. If I start a simulations with collisions on, it still generates further ionization at places where charge states were already high.

Regards
--Sijoy C.D.

[TomGoffrey]

I'm a little confused. Is the problem that you are unable to specify your initial conditions, or that having specified your initial conditions you find the charge state evolves?

[cjoycd]

Sorry for the confusion.

The main issue is that I am unable to prescribe the desired initial condition properly. This would require a charge state (ionization level) for a given species that varies spatially. In my case this varies from unity to nearly fully ionized charge states.

Regards
--Sijoy C.D.

[TomGoffrey]

Thanks for the clarification.

As I said in my initial reply, you'll need to know the spatial variation in number density for each of the ionised species, rather than just the profile of the average charge state. Do you know this?

If it's a simple functional form you can specify a profile as I initially suggested, which would give you Z(x) = n_0 e^{-x}.

If the number densities of each species isn't a functional form then the best option would be to specify the initial conditions from an external file.

Which of these best fits your case?

[cjoycd]

As I mentioned earlier, I already know the spatial variation of both ne and ni. I also know how to incorporate this via input deck specifying the variations as a function spatial co-ordinate, say x. The issue is to specify Z as a function of x, Z(x). To clarify the situation, I have attached a pdf file with a very simplified ne, ni and Z profiles that I require to input. Here, Z(x) is like a step function, and corresponding ne(x) is also a step like function (3 regions) in x. For simplicity I have assumed the ni(x) as constant throughout the space. At any location, the ne(x) = Z(x) * ni(x), and the quasi-neutrality is valid. All these are for a single species. Now, I can specify both ne(x) and ni(x) using some functional form in the input.deck. But as of now there is no way to specify the Z(x) consistent to ne(x) and ni(x), it only takes a constant Z value for a given species.

For a simple case, like the above, I can also specify 3 different species for 3 step regions, and specify ni(x) according to the region where it is, and atomic number, mass number as same for all three regions (species). Also, a constant Z = Z1 (const) for species one and region one, Z = Z2 (const) for species two and region two, ....

Untitled 1.pdf

Another doubt, Is it internally the code calculate Z(x) = ne(x)/ni(x) initially, or it only takes a constant value for a given species initially via input.deck.

Regards
--Sijoy C.D.

[TomGoffrey]

The code doesn't internally calculate Z(x) at all - it doesn't calculate the charge state at all, it's not used by the code. EPOCH assumes an initially quasi-neutral plasma, and then evolves the evolution of the electric field using Ampere's law.

I'm afraid I'm still not clear what you need help with. Perhaps you could post the set-up you are trying to use as initial conditions?

[cjoycd]

Dear Sir,

Sorry for the confusion. By charge state (in continuum cases), I mean the charge (ionization state) of the ion. In the PIC discrete case, this corresponds to the ion charge. I have provided few different initialization cases below. For each case, I have tried to keep ne = Z * ni, making quasi-neutrality valid.

case 1)

begin:species
name = Electron
charge = -1.0
mass = 1.0
number_density = 1.e4
end:species

begin:species
name = Carbon
charge = 1.0
mass = 1836.0 * 12
number_density = number_density(Electron)
end:species

case 2)

begin:species
name = Electron
charge = -1.0
mass = 1.0
number_density = 2.e4
end:species

begin:species
name = Carbon
charge = 2.0
mass = 1836.0 * 12
number_density = number_density(Electron)
end:species

case 2)

begin:species
name = Electron
charge = -1.0
mass = 1.0
number_density = 2.e4
end:species

begin:species
name = Carbon
charge = 1.0
mass = 1836.0 * 12
number_density = number_density(Electron) * 2.0
end:species

I hope the above are correct and valid input conditions ?

I will provide the actual profiles to be generated in due course, once I simplified the profile.

Thanks & Regards
--Sijoy C.D.

[cjoycd]

Dear Sir,

Please find attached for more details of the profile that has to be specified through input.deck.

Thanks & Regards

doubt.pdf