Laser–plasma models

Backscatter(fractions)

Per-group backscattered power fraction (SRS + SBS), removed before deposition. fractions maps a beam group to a number, a function t -> fraction, or a (times, values) table (ns); groups not listed lose nothing. Typically set from measured FABS/NBI backscatter per cone.

Backscatter(:inner23 => 0.10, :inner30 => ([0, 5, 8], [0.0, 0.05, 0.12]))

CalibratedTransfer(donors, receivers, fraction)

Empirical cross-beam transfer: a fraction of the total power of the donors groups moves to the receivers groups (shared in proportion to each receiving beam's power). fraction(Δλ, t) is a calibration — e.g. fit to shot data — where Δλ = ⟨dlambda⟩_receivers − ⟨dlambda⟩_donors (Å, power-weighted means), so a positive Δλ means the receivers are red-shifted relative to the donors, the direction that drives transfer toward them. Total power is conserved.

Build fraction with linear_transfer or tabulated_transfer, or pass any differentiable function.

LaserPlasmaModel

Supertype of laser–plasma corrections. Implement apply_lpi(model, beams, time) returning beams with modified powers (same order, ports and pointing).

apply_lpi(model, beams, time = 0.0) -> Vector{Beam}

Effective beams after the laser–plasma model (nothing = no correction). A tuple or vector of models is applied in order.

linear_transfer(f0, slope; range = (0, 1))

fraction(Δλ, t) = clamp(f0 + slope·Δλ, range...) (slope per Å).

lpi_summary(setup, effective) -> Dict{Symbol,NamedTuple}

Per-group setup and effective power (TW) and their ratio.

tabulated_transfer(Δλs, fractions)

Piecewise-linear fraction(Δλ, t) through the table, constant beyond its ends.

Fully ionized CH (1:1): [(0.5, 6, 12.011), (0.5, 1, 1.008)].

CBET(; leh_z, ne_nc = 0.06, Te = 5000, Ti = 1500, ions = CH_IONS, mach = 1.0,
     flow = nothing, length = 1.5, polarization = :smoothed, multiplier = 1.0,
     nsteps = 20)

Reduced steady-state CBET among the beams that share each laser entrance hole, applied as a laser–plasma model (apply_lpi, Scenario(...; lpi)).

• leh_z — z (mm) of the LEH planes; beams whose ports have z > 0 cross at +leh_z, the rest at -leh_z.
• Plasma in the crossing region: ne_nc (electron density over the critical density at the nominal wavelength), Te, Ti (eV), and ion species ions ((fraction, Z, A) number fractions; default fully ionized CH). Defaults are the NIF LEH conditions of Michel et al. 2009; Ti is not given there and is an assumption.
• flow — outflow speed along the hohlraum axis (km/s, away from the hohlraum), or mach times the ion sound speed √((Z̄ Te + 3 Ti)/(Ā m_p)) when flow is nothing.
• length — maximum interaction length (mm). A pair crossing at angle θ interacts over min(length, w/sin θ), with w the mean beam width at the LEH plane.
• polarization — :smoothed (NIF polarization smoothing, uncorrelated speckle: gain × (1+cos²θ)/4) or :parallel (co-polarized, gain × 1).
• multiplier — calibration factor on all gains. Fit it to shot data: published NIF designs tune CBET with saturation clamps and power multipliers.
• clamp — ion-wave saturation level δn/n (nothing = linear theory, which grossly overpredicts transfer at NIF intensities). Each pair's coupling is multiplied by 1/√(1 + (δn/clamp)²), a smooth version of capping the linear δn/n at clamp. Published NIF calibrations range from 3×10⁻⁴ (2011) to 0.002 (foot) / 0.0075 (peak) for N221204 (Kritcher et al., PRE 109, 025204, 2024); default 0.002.

Any plasma parameter and multiplier may be a number, a function of time (ns), or a (times, values) table. Each pair's exchange uses the geometric-mean beam area at the LEH, so total power is conserved. The coupled exchange is integrated with nsteps RK4 steps. Beam detuning comes from Beam.dlambda (Å at the beam's own wavelength — NIF quotes Δλ at 1ω, so divide those values by 3 for 3ω beams).

calibrate_cbet(model, beams, data; receivers, fit = (:multiplier,), time = 0.0,
               bounds = Dict(:multiplier => (1e-3, 10.0), :mach => (0.0, 3.0),
                             :clamp => (1e-4, 0.05))) -> (model, result)

Fit CBET calibration parameters to measured or reference transfer data. data is a list of (dlambda, ratio) pairs: with the receivers groups (e.g. the inner cones) detuned by dlambda (Å, beam wavelength — 1ω-quoted NIF values ÷ 3), their total power should be multiplied by ratio (e.g. 1.6 for "inner +60%"). Fits the constant-valued fields in fit (any of :multiplier, :mach, :clamp) by bounded L-BFGS-B on squared log-ratio residuals with automatic-differentiation gradients. Returns the calibrated model and the Optim result.

cbet_coupling(Ω, k, kdotu; ne, Te, Ti, ions) -> Γ

Ion-acoustic response Γ = χe(1+χi)/(1+χe+χi) for beat frequency Ω (rad/s), beat wavenumber k (1/m), Doppler shift k·u (rad/s), electron density ne (m⁻³), temperatures Te, Ti (eV), and ion species ions — (fraction, Z, A) tuples with number fractions summing to one; χi sums over species (each with its own Landau damping, which matters for CH: the protons dominate).

cbet_gain(m, b, c, t) -> g

Linear (unsaturated) spatial gain rate (1/mm per TW/mm² of beam c) of beam b due to beam c crossing at the LEH, at time t, including the polarization factor and multiplier. Antisymmetric: cbet_gain(m, c, b, t) == -cbet_gain(m, b, c, t).

Plasma parameters of m at time t as a NamedTuple (SI densities, eV, m/s flow).

ion_wave_amplitude(m::CBET, b, c, t = 0.0) -> δn/n

Linear ion-acoustic density perturbation driven by beams b and c at their LEH plane intensities — compare with m.clamp.

plasma_dispersion(ξ) -> Complex

Fried–Conte plasma dispersion function for real argument, Z(ξ) = −2 D(ξ) + i√π exp(−ξ²) (D: Dawson's integral). Differentiable.

receiver_ratio(model, beams, dlambda; receivers, time = 0.0)

Ratio of the receivers groups' total power after/before model when those groups are detuned by dlambda (Å, beam wavelength) and all other beams by zero.