ParticleBinning diagnostic for pressure

[Tissot11]

I have found inconsistency while calculating Pxx for calculating the temperatures using the Particle Binning diagnostics. I have initialised electrons and ions using the same temperature and density profiles. While I get the correct results for electrons (Txx, Tyy, Tzz) but for ions, I get incorrect results only for Pxx or Txx. Tyy and Tzz for ions are correct too. I have already adjusted for ion mass factor. Both the values and the profile (x<0) for Txx component of ions is incorrect at the initialisation. Txx is supposed to have the same profile like for other components and other species.

I am a bit perplexed by this inconsistency. How to understand this? I do have a drift in x-direction for both electron and ions. Below are the snippets for electrons and ions diagnostics

DiagParticleBinning(
     name = "densEon",
     deposited_quantity = "weight",
     every = everyDiag,
     time_average = 1,
     species = ["eon1", "eon2"],
     axes = [
            ["x", 0.0, Lx, 4096],
            ],
)
DiagParticleBinning(
     name = "TxxEon",
     deposited_quantity = "weight_vx_px",
     every = everyDiag,
     time_average = 1,
     species = ["eon1", "eon2"],
     axes = [
        ["x", 0.0, Lx, 4096],
           ],
)
DiagParticleBinning(
     name = "TyyEon",
     deposited_quantity = "weight_vy_py",
     every = everyDiag,
     time_average = 1,
     species = ["eon1", "eon2"],
     axes = [
          ["x", 0.0, Lx, 4096],
            ],
)
DiagParticleBinning(
     name = "TzzEon",
     deposited_quantity = "weight_vz_pz",
     every = everyDiag,
     time_average = 1,
     species = ["eon1", "eon2"],
     axes = [
          ["x", 0.0, Lx, 4096],
            ],
)
DiagParticleBinning(
     name = "densIon",
     deposited_quantity = "weight",
     every = everyDiag,
     time_average = 1,
     species = ["ion1", "ion2"],
     axes = [
          ["x", 0.0, Lx, 4096],
            ],
)
DiagParticleBinning(
     name = "TxxIon",
     deposited_quantity = "weight_vx_px",
     every = everyDiag,
     time_average = 1,
     species = ["ion1", "ion2"],
     axes = [
          ["x", 0.0, Lx, 4096],
            ],
)
DiagParticleBinning(
     name = "TyyIon",
     deposited_quantity = "weight_vy_py",
     every = everyDiag,
     time_average = 1,
     species = ["ion1", "ion2"],
     axes = [
          ["x", 0.0, Lx, 4096],
           ],
)
DiagParticleBinning(
     name = "TzzIon",
     deposited_quantity = "weight_vz_pz",
     every = everyDiag,
     time_average = 1,
     species = ["ion1", "ion2"],
     axes = [
          ["x", 0.0, Lx, 4096],
            ],
)

[mccoys]

Hi @Tissot11

I moved this to the discussions as I don't think this is a bug. I believe your result is related to the fact that the definition you are using in your Pxx diagnostic (weight_vx_px) does not provide exactly what you seek.

weight_vx_px divided by weight essentially provides the average of $v_{x} p_{x}$ whereas the pressure is correctly defined as the average of $(v_{x}-\langle v_x\rangle) (p_{x}-\langle p_x\rangle)$. As this latter average is equal to $\langle v_x p_x\rangle - \langle v_x\rangle\langle p_x\rangle$, one solution to your problem would be to make separate diagnostics for $\langle v_x\rangle$ and $\langle p_x\rangle$. You can perform the operation during post-processing.

Note of course that $\langle v_x\rangle$ and $\langle p_x\rangle$ are equal to a constant factor when non-relativistic.

[Tissot11]

Thanks. Since the default categories are either Bug or Feature Request for submitting a new issue, I choose Bug.

Both electrons and ions have the same non-relativistic drifts (mean velocities) in x direction, so it is a bit perplexing that electrons diagnostic gives correct results while ion diagnostics does not. Is it because, the ion momentum is scaled in terms of electrons mass scale, making it relativistic in terms of electron momentum? Of course, I can create separate diagnostics and do the stuff in post-processing.

[mccoys]

Yes the difference with electrons might be related to relativistic velocity. I am not sure though.

[Tissot11]

Do you think, this would work?

def stuff(particles):
    return particles.weight * (particle.vx*particles.px)

and subtract this stuff from weight_vx_px in post-processing. Or this stuff is actually weight_vx_px diagnostic?