Solver Reference

Solver Reference

Every solver accepts a plain config struct and returns a results struct. Omitted fields fall back to the defaults listed here. All inputs use SI units unless the name says otherwise (*_C fields are degrees Celsius, *_um micrometers).

Fields shared by all solvers:

Field	Default	Meaning
makePlots	true	draw diagnostic figures
saveFigures	false	save figures to the output folder (forces makePlots = true)
outputDir	solver-specific folder under outputs/	where text reports and figures are written

Returned fields shared by all solvers: solver, solverId, contractVersion, material, outputFile, outputDir, inputConfig, plus nPulses and wallTime_s where meaningful. See Results and Outputs.

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Surface_Point_Solver

results = Surface_Point_Solver(cfg)

0D surface-point TTM. Fastest entry point for pulse-accumulation studies and parameter sweeps. Solves the coupled electron-lattice equations at the surface during each pulse, then runs 1D Crank-Nicolson diffusion into depth for the inter-pulse gap.

Field	Default	Unit	Meaning
material	'W'		'W', 'Cu', 'Au', 'Al', or 'custom'
Pavg	1	W	average laser power
spotRadius	80e-6	m	1/e^2 Gaussian spot radius
f_rep	1e6	Hz	repetition rate
tau_FWHM	500e-15	s	pulse width (FWHM for Gaussian)
pulseProfile	'gaussian'		'gaussian', 'square', or 'exp'
simDuration	100e-6	s	total simulated time; pulse count is simDuration * f_rep
absorbance	0.55		surface absorbance A, 0 to 1
Leff	100e-9	m	effective heated thickness for the 0D energy balance
T0_C	25	degC	initial temperature
depthProfile	'exponential'		initial depth profile handed to inter-pulse diffusion, 'box' or 'exponential'
dzTarget	500e-9	m	diffusion grid spacing
Ndiff	100		Crank-Nicolson steps per inter-pulse period
gamma_manual, Cl_manual, G_manual, kl_manual	see file		material properties used when material = 'custom'

Key returned fields beyond the shared contract: full surface histories time_s, Te_K, Tl_K, Te_C, Tl_C; per-pulse arrays TeqVals_C and TresidVals_C; peakTe_C, peakTl_C, finalResid_C, projectedSteadyState_C; energy bookkeeping absorbedAreal_J_m2, depthEnergy_J_m2, energyMismatch_pct.

---

Depth_Profile_Solver

results = Depth_Profile_Solver(cfg)

The main 1D depth-resolved multi-pulse solver. Solves the coupled electron-lattice PDEs along depth with ode15s during each pulse (Phase 1), then maps the end state to a coarser, deeper grid and diffuses it with Crank-Nicolson for the inter-pulse gap (Phase 2). This is the solver that resolves the surface temperature inversion.

Field	Default	Unit	Meaning
material	'W'		'W', 'Cu', 'Al', or 'custom'
Pavg	40	W	average laser power
spotRadius	100e-6	m	1/e^2 spot radius
f_rep	18e6	Hz	repetition rate
tau_FWHM	100e-15	s	pulse width (FWHM)
pulseProfile	'gaussian'		'gaussian', 'square', or 'exp'
simDuration	100e-6	s	total simulated time; pulse count is simDuration * f_rep
absorbance	0.55		surface absorbance
T0_C	25	degC	initial temperature
Lz	1000e-9	m	Phase 1 simulation depth
Nz	200		Phase 1 spatial nodes; keep dz at or below a quarter of the optical skin depth
snapshotDelays	0 to 200 ps set	s	delays for spatial profile snapshots, relative to the first pulse center
enableRadialProfile	true		derive radial surface profiles from the depth solution
Nr_radial	20		radial points when enableRadialProfile is on
rMax_factor	3		radial extent as a multiple of spotRadius
dzTarget_diff	500e-9	m	Phase 2 coarse-grid spacing
Ndiff	100		Phase 2 Crank-Nicolson steps per inter-pulse period
relTol, absTol	1e-6, 0.1		ode15s tolerances (absTol in kelvin)
gamma_manual, Cl_manual, G_manual, ke0_manual, kl_manual, alpha_opt_manual	see file		properties for material = 'custom'

Key returned fields: per-pulse arrays TePeakPerPulse_C, TlPeakPerPulse_C, TeqVals_C, TresidVals_C, baseTempPerPulse_C; inversion metrics invMaxPerPulse_K, tMaxInvPerPulse_s, tInvOnsetPerPulse_s, invDurationPerPulse_s, Te_atMaxInvPerPulse_C, Tl_atMaxInvPerPulse_C; the resolved input set (f_rep, Pavg, tau_FWHM, spotRadius, absorbance, F_peak, gamma, Cl, G, ke0, kl, alpha_opt).

---

Radial_Profile_Solver

results = Radial_Profile_Solver(cfg)

Radial surface-temperature solver under a Gaussian beam. Two modes:

• 'scale' (default, fastest): one 0D solve at beam center, scaled radially by the Gaussian fluence profile. Valid when the spot radius is much larger than the lateral diffusion length.
• 'independent': a separate 0D solve at each radial node. Roughly Nr times slower, but captures the nonlinear electron heat capacity response at different local fluences.

Field	Default	Unit	Meaning
material	'W'		'W', 'Cu', 'Al', or 'custom'
Pavg	40	W	average laser power
spotRadius	100e-6	m	1/e^2 spot radius
f_rep	18e6	Hz	repetition rate
tau_FWHM	100e-15	s	pulse width (FWHM)
pulseProfile	'gaussian'		temporal profile
simDuration	1e-3	s	total simulated time
absorbance	0.55		surface absorbance
Leff	100e-9	m	effective heated thickness
T0_C	25	degC	initial temperature
Nr	80		radial nodes from the beam axis to rMax
rMax_factor	5		radial extent as a multiple of spotRadius
radialSolveMode	'scale'		'scale' or 'independent'
earlyStopMeltRadius_um	0	um	if positive, stop when the predicted melt radius reaches this value
earlyStopT_melt_C	3422	degC	melt temperature used by the early-stop check
earlyStopCheckInterval	100		pulses between early-stop checks
depthProfile, dzTarget, Ndiff	as 0D solver		inter-pulse diffusion settings

Key returned fields: rGrid_um, finalRadialProfile_C, spotRadius_um, peakTeq_C, finalResid_C, mode.

---

Single_Pulse_Visualizer

results = Single_Pulse_Visualizer(cfg)

One pulse of the 1D depth-resolved TTM with spatial snapshots at chosen delays. Useful for inspecting early-time behavior and generating teaching figures. Accepts the same material and laser fields as Depth_Profile_Solver (defaults differ: Pavg = 1 W, spotRadius = 80e-6 m, f_rep = 1e6 Hz, tau_FWHM = 100e-15 s), plus:

Field	Default	Unit	Meaning
Lz	1000e-9	m	simulation depth
Nz	200		spatial nodes
snapshotDelays	[0, 0.5, 1, 2, 5, 10, 50, 200] ps	s	delays for Te(z) and Tl(z) profile snapshots
relTol, absTol	1e-6, 0.1		ode15s tolerances

Key returned fields: peakTe_C, peakTl_C, finalTe_C, finalTl_C, invDetected, maxInv_C.

---

Inversion_Quantifier

results = Inversion_Quantifier(cfg)

Post-processing layer over Depth_Profile_Solver that quantifies the electron-lattice temperature inversion across pulses: magnitude, onset time, duration, and trends against the accumulating base temperature.

Accepts the same fields as Depth_Profile_Solver, plus:

Field	Default	Meaning
depthResults	none	pre-computed Depth_Profile_Solver results struct; when supplied, the depth solve is skipped

Key returned fields: nInvPulses, meanInv_K, maxInv_K, minInv_K, stdInv_K, invSlope_KperPulse, corrBaseTempInv, meanInvFraction, and the per-pulse arrays invMaxPerPulse_K, TePeak_C, TlPeak_C, Tbase_C.

---

Scanning_Beam_Solver

results = Scanning_Beam_Solver(params, outputDir, savePlots)

Moving-beam surface model. Combines scanning kinematics (spot velocity, repetition rate) with per-pulse heating and inter-pulse surface diffusion to build the 2D temperature footprint of a scanned line. Note the interface: a params struct plus two optional positional arguments instead of a single cfg.

Field	Default in example	Unit	Meaning
material	'W'		preset or 'custom' (with gamma, Cl, G, kl fields)
Pavg	40	W	average laser power
spotRadius	100e-6	m	1/e^2 spot radius
f_rep	18e6	Hz	repetition rate
tau_FWHM	100e-15	s	pulse width
pulseProfile	'gaussian'		temporal profile
v_scan	1.0	m/s	scan speed
scanLength	2e-3	m	scanned line length; pulse count is scanLength * f_rep / v_scan
absorbance	0.55		surface absorbance
Leff	100e-9	m	effective heated thickness
T0_C	25	degC	initial temperature
Nx, Ny	120, 60		surface grid resolution
xPad	3		x-extent padding in spot radii beyond the scan line
yExtent	5		y-extent in spot radii
depthProfile, dzTarget, Ndiff, NadiPerGap	'exponential', 500e-9, 100, 10		depth and diffusion controls

Key returned fields: Tpeak_map (peak temperature at each surface point), Tsurf (final surface field), peakT_history, xGrid, yGrid, pulseSpacing, dTeq_single, and a saved .mat snapshot path in matPath.

The baseline example (2 mm at 1 m/s and 18 MHz) simulates 36,000 pulses and takes several minutes.