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<p>Ultrafast laser processing at megahertz repetition rates produces cumulative inter-pulse heat buildup that governs damage thresholds, melt onset, and surface quality. The two-temperature model (TTM) resolves the nonequilibrium electron–lattice physics of each pulse, but becomes impractical for multi-pulse sequences typical of MHz-rate processing. We present a two-stage decoupling method that separates each pulse cycle into a stiff TTM integration during the pulse and relaxation period, followed by Crank–Nicolson diffusion through the inter-pulse gap using temperature-dependent thermal conductivity from tabulated data. Applied to tungsten, the solver completes a 10,000-pulse simulation in under 17&#xa0;min on a single workstation, approximately 600 times faster than the most efficient previously reported spatially resolved multi-pulse TTM. Multi-pulse simulations predict progressive inter-pulse temperature buildup and a growing surface temperature inversion (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(T_{{\text{l}}} &gt; T_{{\text{e}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>T</mi> <mtext>l</mtext> </msub> <mo>&gt;</mo> <msub> <mi>T</mi> <mtext>e</mtext> </msub> </mrow> </math></EquationSource> </InlineEquation>). A fixed-energy parametric study shows that heat accumulation transitions from negligible to severe between 1 and 10&#xa0;MHz, consistent with the thermal diffusion timescale. Validation against a cross section of a melting-regime tungsten track (70&#xa0;W, 40&#xa0;MHz, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(w_{0} = 150\;\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>w</mi> <mn>0</mn> </msub> <mo>=</mo> <mn>150</mn> <mspace width="0.277778em" /> </mrow> </math></EquationSource> </InlineEquation> μm) shows that the predicted melt zone diameter of 200&#xa0;μm matches the grain-coarsened zone in the SEM cross section.</p>

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A Computationally Efficient Two-Stage Two-Temperature Model for Multi-pulse Femtosecond Laser Heat Accumulation in Tungsten

  • 期刊论文

  • 发表日期：

    2026年8月5日

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  • David Fieser,
  • Unmanaa Nileen Dewanjee,
  • Anming Hu

摘要

Ultrafast laser processing at megahertz repetition rates produces cumulative inter-pulse heat buildup that governs damage thresholds, melt onset, and surface quality. The two-temperature model (TTM) resolves the nonequilibrium electron–lattice physics of each pulse, but becomes impractical for multi-pulse sequences typical of MHz-rate processing. We present a two-stage decoupling method that separates each pulse cycle into a stiff TTM integration during the pulse and relaxation period, followed by Crank–Nicolson diffusion through the inter-pulse gap using temperature-dependent thermal conductivity from tabulated data. Applied to tungsten, the solver completes a 10,000-pulse simulation in under 17 min on a single workstation, approximately 600 times faster than the most efficient previously reported spatially resolved multi-pulse TTM. Multi-pulse simulations predict progressive inter-pulse temperature buildup and a growing surface temperature inversion ( \(T_{{\text{l}}} > T_{{\text{e}}}\) T l > T e ). A fixed-energy parametric study shows that heat accumulation transitions from negligible to severe between 1 and 10 MHz, consistent with the thermal diffusion timescale. Validation against a cross section of a melting-regime tungsten track (70 W, 40 MHz, \(w_{0} = 150\;\) w 0 = 150 μm) shows that the predicted melt zone diameter of 200 μm matches the grain-coarsened zone in the SEM cross section.