Does the QDSMC cell-center-to-node remap introduce cumulative electron-entropy diffusion?

[tomzhu0225]

I am seeing a broad electron-temperature “foot” ahead of an imploding plasma shell when using the Hybrid-PIC electron-energy equation. I am posting this as a question rather than a bug report because the simulation uses experimental RCYLINDER QDSMC support on feature/hybrid-implicit-mag-diffusion; RCYLINDER QDSMC is still disabled on development. However, the gather/deposit mechanism below appears geometry-independent away from an axis or boundary.

Observation

At approximately 40 ns, the Hybrid-PIC result has elevated electron temperature throughout the unshocked 4–10 mm region, while an otherwise matched implicit-kinetic reference remains mostly cold there. Correcting the independent radial-unit errors in the per-species fields removes the on-axis mode but does not remove this broad foot.

Possible numerical mechanism

The current QDSMC path:

1. initializes one marker at each cell center;
2. linearly gathers the nodal density and entropy to that marker; and
3. linearly deposits the carried values back to the nodes.

For uniform marker weights in one dimension, even with zero marker displacement, this gather/deposit pair appears to apply

$$ K_i^{n+1}=\frac14K_{i-1}^n+\frac12K_i^n+\frac14K_{i+1}^n. $$

It is therefore not the identity map for a nonuniform nodal entropy field. Repeating it every PIC step gives an estimated smoothing length

$$ L\sim\Delta r\sqrt{N/4}. $$

For this case, Delta r = 0.125 mm and N = 5120 at 40 ns, giving L ≈ 4.5 mm, comparable to the observed foot width.

Controlled tests

I added temporary diagnostic switches on the feature branch to isolate the operations. These are not proposed input parameters or fixes.

40 ns case	Mean Te, 4–10 mm	Interpretation
Implicit kinetic	2.09 eV	Reference
Full QDSMC control	8.01 eV	Broad foot
QDSMC gather/deposit, but marker push bypassed	7.78 eV	97% of the control foot remains without advection
Twice the timestep / half as many remaps	6.52 eV	Foot decreases with remap count
QDSMC remap bypassed	1.43 eV	Foot removed, but coupled shell dynamics degrade

The radial marker-volume control remains close to the full control. Physical radial volume weighting is independently necessary (see #7130), but it does not make the cell-center-to-node remap an identity operation.

Disabling the marker push rules out physical electron-fluid advection as the main source of this broad structure. Bypassing the remap is only a diagnostic: it changes the intended entropy transport and worsens the density/field trajectory, so I am not proposing it as a solution.

Questions

1. Is this zero-displacement smoothing an expected numerical property of the QDSMC scheme, or should the gather/deposit cycle preserve an arbitrary nodal K_e field when the markers do not move?
2. Is the combination of cell-centered marker home positions and nodal K_e intentional?
3. Would a stationary, nonuniform-entropy test in a currently supported Cartesian or RZ geometry be the right minimal reproducer before opening an issue?
4. If identity preservation is required, what remap approach would be consistent with the intended QDSMC discretization and conservation properties?

This is separate from physical electron heat conduction: the documented QDSMC model neglects conductive heat flux. The concern here is additional numerical entropy transport observed when marker advection is bypassed.

[roelof-groenewald]

Hi @tomzhu0225, is the issue your seeing here related to the fix from #7128 or is it a separate problem?

[tomzhu0225]

It is a separate problem. The code links and controlled runs in this discussion use 0b1d055, which is the merge commit of #7128, so they already include that fix.

#7128 removes the below-floor heat sink: low-density cells no longer seed or erase zero entropy, and its uniform-entropy test is invariant under mixing. The effect here starts from a nonuniform nodal K_e field and remains when the marker push is bypassed. For stationary cell-centered markers, the linear nodal gather followed by linear redeposition applies the [1/4, 1/2, 1/4] stencil rather than the identity, including away from the density floor and axis.

The two mechanisms can interact at a plasma edge, but #7128 addresses entropy loss at the floor whereas this discussion concerns cumulative remap smoothing of resolved entropy gradients. A stationary nonuniform-entropy test in a supported geometry would be the next focused reproducer.