Add relative permittivity (epsilon_r) to Ampere's law

[tomzhu0225]

Summary

This PR adds a warpx.epsilon_r parameter that introduces a uniform relative permittivity into Ampere's law, scaling the curl(B) and J terms by 1/epsilon_r. This effectively reduces the EM wave propagation speed to c/sqrt(epsilon_r) and relaxes the CFL condition for explicit FDTD simulations.

Faraday's law and the particle pusher are not modified.

Issue #6769. Supersedes #6725.

Motivation

In high-density plasma simulations (e.g., Z-pinch, dense fusion targets), the light-wave CFL constraint can be orders of magnitude more restrictive than needed by the plasma dynamics. This feature allows users to relax the CFL by a factor of sqrt(epsilon_r) while keeping the explicit FDTD solver.

Changes from #6725

PR #6725 implemented this as a "reduced speed of light" by globally replacing PhysConst::c with a modified WarpX::c_light across 14 files. Per reviewer feedback, this PR reframes the approach as adding a relative permittivity to Ampere's law, which:

• Does not redefine or shadow any physical constant
• Confines modifications to the Ampere equation and related routines only
• Is physically equivalent: setting epsilon_r = N² gives the same result as c → c/N

Physics

Standard Ampere's law:

$$\frac{\partial \mathbf{E}}{\partial t} = c^2 \nabla \times \mathbf{B} - \frac{\mathbf{J}}{\epsilon_0}$$

With warpx.epsilon_r:

$$\frac{\partial \mathbf{E}}{\partial t} = \frac{c^2}{\epsilon_r} \nabla \times \mathbf{B} - \frac{\mathbf{J}}{\epsilon_0 , \epsilon_r}$$

Faraday's law $\partial \mathbf{B}/\partial t = -\nabla \times \mathbf{E}$ is unchanged.

Implementation

File	Change
WarpX.H / WarpX.cpp	Declare, initialize, and parse epsilon_r with safeguards
EvolveE.cpp	c2 → c2 / epsilon_r (Cartesian, Cylindrical, Spherical)
EvolveEPML.cpp	c2 → c2 / epsilon_r, mu_c2_dt scaled
EvolveG.cpp	c2 → c2 / epsilon_r (div cleaning)
MacroscopicEvolveE.cpp	beta → beta / epsilon_r
WarpXComputeDt.cpp	dt *= sqrt(epsilon_r)
ApplySilverMuellerBoundary.cpp	c → c / sqrt(epsilon_r) for ABC impedance matching
parameters.rst	Document warpx.epsilon_r
Examples/Tests/epsilon_r/	1D Z-pinch test case

Safeguards

• epsilon_r >= 1.0 enforced at runtime
• Only allowed with algo.evolve_scheme = explicit
• Rejected for PSATD and HybridPIC solvers
• Informational message printed when epsilon_r > 1

Test

A lightweight 1D Z-pinch test (test_1d_epsilon_r) with epsilon_r = 100.0 verifies that the parameter is parsed, the CFL is relaxed by a factor of 10, and the simulation runs correctly.

[tomzhu0225]

Friendly reminder on this PR. This version reframes the feature as adding epsilon_r to Ampère’s law, with default behavior unchanged at epsilon_r = 1.0. I’d appreciate any feedback on whether this design looks acceptable for merge.