SpectraRust/src/tlusty/math/continuum/lte_opacity.rs

//! LTE 不透明度的简化物理计算。
//!
//! 使用物理公式计算 Rosseland 和 Planck 平均不透明度，
//! 作为完整表插值方法的替代。
//!
//! # 不透明度来源
//!
//! 1. 电子散射 (Thomson 散射)
//! 2. 束缚-自由跃迁 (氢光致电离，Kramers 截面)
//! 3. 自由-自由跃迁 (氢轫致辐射)
//! 4. H- 不透明度 (负氢离子)
//!
//! # 参考
//!
//! - TLUSTY opacfl.f, meanopt.f
//! - Mihalas (1978) Stellar Atmospheres

use crate::tlusty::state::constants::{H, HK, SIGE};

// ============================================================================
// 物理常数
// ============================================================================

/// 光速 (cm/s)
const CLIGHT: f64 = 2.99792458e10;

/// 氢电离频率 (Hz)
const FRH: f64 = 3.28805e15;

/// H- 自由-自由系数
const CFF1: f64 = 1.3727e-25;
const CFF2: f64 = 4.3748e-10;
const CFF3: f64 = 2.5993e-7;

/// 自由-自由基准截面
const SGFF0: f64 = 3.694e8;

/// H- 电离阈值频率 (Hz)
const FRHM: f64 = 1.82e15;

// ============================================================================
// 数据结构
// ============================================================================

/// LTE 不透明度输入参数
#[derive(Debug, Clone)]
pub struct LteOpacityParams {
    /// 温度 (K)
    pub t: f64,
    /// 电子密度 (cm⁻³)
    pub ne: f64,
    /// 总氢密度 (中性 + 电离) (cm⁻³)
    pub nh_total: f64,
    /// 质子密度 (cm⁻³)
    pub np: f64,
    /// 中性氢密度 (cm⁻³)
    pub nh_neutral: f64,
    /// H- 密度 (cm⁻³)
    pub nhm: f64,
    /// 密度 (g/cm³)
    pub rho: f64,
    /// 氢配分函数
    pub uh: f64,
    /// 氦配分函数
    pub uhe: f64,
    /// He+ 配分函数
    pub uhep: f64,
    /// 氢丰度 (质量分数)
    pub xh: f64,
    /// 氦丰度 (质量分数)
    pub xhe: f64,
}

impl Default for LteOpacityParams {
    fn default() -> Self {
        Self {
            t: 10000.0,
            ne: 1e12,
            nh_total: 1e12,
            np: 5e11,
            nh_neutral: 5e11,
            nhm: 0.0,
            rho: 1e-12,
            uh: 2.0,
            uhe: 1.0,
            uhep: 2.0,
            xh: 0.70,
            xhe: 0.28,
        }
    }
}

/// LTE 不透明度输出
#[derive(Debug, Clone)]
pub struct LteOpacityOutput {
    /// Rosseland 平均不透明度 (cm²/g)
    pub opros: f64,
    /// Planck 平均不透明度 (cm²/g)
    pub oppla: f64,
    /// 电子散射不透明度 (cm²/g)
    pub opes: f64,
    /// 束缚-自由不透明度 (cm²/g)
    pub opbf: f64,
    /// 自由-自由不透明度 (cm²/g)
    pub opff: f64,
    /// H- 不透明度 (cm²/g)
    pub ophm: f64,
}

/// LTE 频率网格
#[derive(Debug, Clone)]
pub struct LteFrequencyGrid {
    /// 频率数组 (Hz)
    pub freq: Vec<f64>,
    /// 权重数组
    pub weights: Vec<f64>,
    /// Planck 函数
    pub bnue: Vec<f64>,
    /// Edge type markers: 1=edge frequency, 2=interior frequency
    /// (from Fortran IJXCO array in INIFRC)
    pub ijxco: Vec<i32>,
    /// IJFR mapping: indices of explicit (non-ALI) frequency points
    /// selected by INIFRC(1)/CORRWM logic for SOLVES.
    /// These are the points near ionization edges.
    pub ijfr: Vec<usize>,
}

// ============================================================================
// 核心计算函数
// ============================================================================

/// 生成用于 LTE 不透明度积分的频率网格。
pub fn generate_lte_frequency_grid(_teff: f64, nfreq: usize) -> LteFrequencyGrid {
    let frmin: f64 = 1e13;
    let frmax: f64 = 3e16;

    let log_frmin = frmin.ln();
    let log_frmax = frmax.ln();
    let dlog = (log_frmax - log_frmin) / (nfreq - 1) as f64;

    let mut freq = Vec::with_capacity(nfreq);
    let mut weights = Vec::with_capacity(nfreq);
    let mut bnue = Vec::with_capacity(nfreq);

    let c1 = 2.0 * H / (CLIGHT * CLIGHT);

    for i in 0..nfreq {
        let log_fr = log_frmin + i as f64 * dlog;
        let fr = log_fr.exp();
        freq.push(fr);

        let w = if i == 0 || i == nfreq - 1 {
            0.5 * dlog * fr
        } else {
            dlog * fr
        };
        weights.push(w);

        // BNUE = (2H/c²)·ν³ — prefactor only (matches Fortran BNUE=BN*ν³, tlusty208.f:30748).
        // The (exp(hν/kT)-1) divisor is applied by consumers at the LOCAL T
        // (plan = bnue * e1 * w, e1=1/(exp(hν/kT_local)-1)). Baking the TEFF divisor in
        // here left a frequency-dependent spurious factor that biased the Rosseland mean.
        bnue.push(c1 * fr.powi(3));
    }

    LteFrequencyGrid { freq, weights, bnue, ijxco: vec![], ijfr: vec![] }
}

/// Ionization edge frequency (Hz) for INIFRC-like grid generation.
#[allow(dead_code)]
struct IonEdge {
    freq: f64,
    label: &'static str,
}

/// Generate an INIFRC frequency grid faithfully reproducing the Fortran INIFRC algorithm.
///
/// Uses the NFTAIL>0 path with:
/// - 2-part linear high-frequency tail with Simpson 1/3 weights
/// - Per-segment weight computation (Simpson for uniform, trapezoidal at edges)
/// - DFTAIL=0.25, NFTAIL=21 (Fortran defaults)
/// - DNX = 1 - 1/(NFREQC/5)
///
/// All 35 unique ionization edge frequencies from the HHe atomic model are included.
pub fn generate_inifrc_frequency_grid(teff: f64, nfreq_base: usize) -> LteFrequencyGrid {
    let frcmax: f64 = 8.0e11 * teff;
    let frcmin: f64 = 1.0e12;
    let dfedg = 0.000001; // Fortran default: dfedg=1e-6 for icompt=0
    let nftail: usize = 21;
    let dftail: f64 = 0.25;
    let njc = (nfreq_base / 5).max(1);
    let dnx = 1.0 - 1.0 / njc as f64;

    // All unique ionization edge frequencies (ENION/H) from HHe model
    // Sorted descending (matching Fortran INDEXX sort order)
    let frlev: Vec<f64> = vec![
        1.3157598e16, // He 2 (N=1)
        5.9450352e15, // He 1 1sS
        3.2893994e15, // He 2 (N=2)
        3.2880500e15, // H 1 (N=1)
        1.4619553e15, // He 2 (N=3)
        1.1526721e15, // He 1 2tS
        9.6014543e14, // He 1 2sS
        8.7593372e14, // He 1 2tP
        8.2201250e14, // H 1 (N=2)
        8.1453622e14, // He 1 2sP
        5.2630391e14, // He 2 (N=5)
        4.5172735e14, // He 1 3tS
        4.0292112e14, // He 1 3sS
        3.8193564e14, // He 1 3tP
        3.6583679e14, // He 1 3tD
        3.6574687e14, // He 1 3sD
        3.6548882e14, // He 2 (N=6)
        3.6533889e14, // H 1 (N=3)
        3.6259902e14, // He 1 3sP
        2.6852240e14, // He 2 (N=7)
        2.4004386e14, // He 1 4tS
        2.2058746e14, // He 2 (N=8)
        2.2079719e14, // He 1 4sS
        2.1249294e14, // He 1 4tP
        2.0550313e14, // H 1 (N=4)
        1.6243948e14, // He 2 (N=9)
        1.3152200e14, // H 1 (N=5)
        1.3157598e14, // He 2 (N=10)
        1.0874048e14, // He 2 (N=11)
        9.1372206e13, // He 2 (N=12)
        9.1334722e13, // H 1 (N=6)
        7.7855608e13, // He 2 (N=13)
        6.7130600e13, // He 2 (N=14)
        6.7103061e13, // H 1 (N=7)
        5.1375781e13, // H 1 (N=8)
    ];
    let nlevel = frlev.len();

    let third = 1.0 / 3.0;
    let fth = 4.0 / 3.0;

    // Use 1-based indexing internally (matching Fortran) for clarity
    // Dynamic Vec that grows as needed (Fortran uses MFREQC=125000)
    let cap = 8192;
    let mut freqco: Vec<f64> = vec![0.0; cap];
    let mut wco: Vec<f64> = vec![0.0; cap];
    let mut ijxco: Vec<i32> = vec![0; cap];

    // Helper: ensure arrays have at least `min_cap` elements
    let ensure_cap = |freqco: &mut Vec<f64>, wco: &mut Vec<f64>, ijxco: &mut Vec<i32>, min_cap: usize| {
        if freqco.len() < min_cap {
            freqco.resize(min_cap, 0.0);
            wco.resize(min_cap, 0.0);
            ijxco.resize(min_cap, 0);
        }
    };

    // Find IL0: first level with FRLEV(IL0) < FRCMAX
    let mut il0: usize = 1;
    while il0 <= nlevel && frlev[il0 - 1] >= frcmax {
        il0 += 1;
    }

    // --- High-frequency tail (Fortran lines 156-223) ---
    let nend = nftail; // = 21
    let divend = dftail; // = 0.25
    let mut nfreqc: usize = nend + 1; // NFREQC starts at NEND+1 = 22

    // Set FREQCO(1) = FRCMAX
    freqco[1] = frcmax;

    // Set edge pair at NEND, NEND+1
    freqco[nend] = (1.0 + dfedg) * frlev[il0 - 1];
    freqco[nend + 1] = (1.0 - dfedg) * frlev[il0 - 1];

    let nend1 = nend / 2 + 1; // = 11
    let xend = 1.0 / (nend1 - 1) as f64; // = 0.1

    // Division frequency
    freqco[nend1] = freqco[1] - (1.0 - divend) * (freqco[1] - freqco[nend]);

    // IJXCO markers
    ijxco[nend + 1] = 1;
    ijxco[1] = 1;
    ijxco[nend1] = 1;

    // Part 1: FREQCO(1) to FREQCO(NEND1), uniform grid
    let d121 = xend * (freqco[1] - freqco[nend1]);
    for ij in 2..=nend1 - 1 {
        freqco[ij] = freqco[ij - 1] - d121;
        ijxco[ij] = 2;
    }

    // Simpson 1/3 weights for part 1
    let d121_3 = third * (freqco[1] - freqco[2]);
    for ij in (2..=nend1 - 1).step_by(2) {
        wco[ij] = 4.0 * d121_3;
        wco[ij - 1] += d121_3;
        wco[ij + 1] += d121_3;
    }

    // Part 2: FREQCO(NEND1) to FREQCO(NEND)
    if nend1 < nend {
        ijxco[nend] = 1;
        ijxco[nend + 1] = 1;
        let d121_p2 = xend * (freqco[nend1] - freqco[nend]);
        for ij in nend1 + 1..=nend - 1 {
            freqco[ij] = freqco[ij - 1] - d121_p2;
            ijxco[ij] = 2;
        }
        let d121_3_p2 = third * (freqco[nend1] - freqco[nend1 + 1]);
        for ij in (nend1 + 1..=nend - 1).step_by(2) {
            wco[ij] = 4.0 * d121_3_p2;
            wco[ij - 1] += d121_3_p2;
            wco[ij + 1] += d121_3_p2;
        }
    }

    // First discontinuity: half-interval weight
    let haend = 0.5 * (freqco[nend] - freqco[nend + 1]);
    wco[nend] += haend;
    wco[nend + 1] += haend;

    // IL0=2 for main loop (Fortran line 233: IL0=2)
    il0 = 2;

    // FRCLST: lowest edge above FRCMIN
    let mut il_last = nlevel;
    while il_last > 1 && frlev[il_last - 1] < frcmin {
        il_last -= 1;
    }
    let frclst = frlev[il_last - 1];

    let xend_main = 1.0 / (nend - 1) as f64;

    // --- Main loop (Fortran label 100) ---
    loop {
        // Ensure arrays have room for next iteration (max + nend + 2)
        ensure_cap(&mut freqco, &mut wco, &mut ijxco, nfreqc + nend + 4);

        let frc0 = dnx * freqco[nfreqc];

        if frc0 < frclst {
            // Insert edge pair at FRCLST, then linear tail to FRCMIN
            nfreqc += 2;
            freqco[nfreqc - 1] = (1.0 + dfedg) * frclst;
            freqco[nfreqc] = (1.0 - dfedg) * frclst;
            ijxco[nfreqc - 1] = 1;
            ijxco[nfreqc] = 1;

            wco[nfreqc] += 0.5 * (freqco[nfreqc - 1] - freqco[nfreqc]);
            wco[nfreqc - 1] += 0.5 * (freqco[nfreqc - 2] - freqco[nfreqc]);
            wco[nfreqc - 2] += 0.5 * (freqco[nfreqc - 2] - freqco[nfreqc - 1]);

            // Linear tail
            let d_tail = xend_main * (freqco[nfreqc] - frcmin);
            let tail_start = nfreqc + 1;
            for ij in tail_start..=nfreqc + nend - 1 {
                freqco[ij] = freqco[ij - 1] - d_tail;
                ijxco[ij] = 2;
            }
            ijxco[nfreqc + nend - 1] = 1;
            for ij in (nfreqc + 1..=nfreqc + nend - 2).step_by(2) {
                wco[ij] = fth * d_tail;
                wco[ij - 1] += third * d_tail;
                wco[ij + 1] += third * d_tail;
            }
            nfreqc = nfreqc + nend - 1;
            break;
        }

        let df0 = frlev[il0 - 1] + 0.1 * (freqco[nfreqc] - frc0);
        let frtl = (1.0 + dfedg) * frlev[il0 - 1];

        if frc0 > df0 {
            // Case 1: regular stepping
            nfreqc += 1;
            freqco[nfreqc] = frc0;
            ijxco[nfreqc] = 2;
            wco[nfreqc] += 0.5 * (freqco[nfreqc - 1] - freqco[nfreqc]);
            wco[nfreqc - 1] += 0.5 * (freqco[nfreqc - 1] - freqco[nfreqc]);
        } else if frtl < freqco[nfreqc] {
            // Case 2: edge pair
            nfreqc += 2;
            freqco[nfreqc - 1] = frtl;
            freqco[nfreqc] = (1.0 - dfedg) * frlev[il0 - 1];
            ijxco[nfreqc - 1] = 1;
            ijxco[nfreqc] = 1;
            wco[nfreqc] += 0.5 * (freqco[nfreqc - 1] - freqco[nfreqc]);
            wco[nfreqc - 1] += 0.5 * (freqco[nfreqc - 2] - freqco[nfreqc]);
            wco[nfreqc - 2] += 0.5 * (freqco[nfreqc - 2] - freqco[nfreqc - 1]);
            il0 += 1;
        } else {
            // Case 3: edge at current position
            il0 += 1;
        }
    }

    // Convert 1-based arrays to 0-based output
    let mut all_freqs: Vec<f64> = Vec::with_capacity(nfreqc);
    let mut all_w: Vec<f64> = Vec::with_capacity(nfreqc);
    let mut all_ijxco: Vec<i32> = Vec::with_capacity(nfreqc);
    for ij in 1..=nfreqc {
        all_freqs.push(freqco[ij]);
        all_w.push(wco[ij]);
        all_ijxco.push(ijxco[ij]);
    }

    let nfreq = all_freqs.len();

    // Compute Planck function prefactor BNUE = (2H/c²)·ν³.
    //
    // IMPORTANT: matches Fortran BNUE (tlusty208.f:30748 `BNUE(IJ)=BN*FR15³`, BN=2H/c²):
    // BNUE is the PREFACTOR ONLY — the (exp(hν/kT)-1) divisor is applied separately
    // at the LOCAL temperature by every consumer (MEANOP, meanopt, lte_meanopt,
    // ltegr call_meanopt all compute `plan = bnue * e1 * w` with e1=1/(exp(hν/kT_local)-1)).
    //
    // Earlier code divided by (exp(hν/kT_eff)-1) here, leaving a frequency-dependent
    // spurious factor that biased the Rosseland mean weight toward low-ν and inflated
    // κ_R at depth (grey-start DM grid too small). The divisor must NOT be baked in.
    let c1 = 2.0 * H / (CLIGHT * CLIGHT);
    let mut bnue = Vec::with_capacity(nfreq);
    for &fr in &all_freqs {
        bnue.push(c1 * fr.powi(3));
    }

    // Compute IJFR: select explicit (non-ALI) frequency points
    // following Fortran INIFRC(1) logic:
    //   For each continuum transition with IFC0=1, IFC1=3:
    //     IJFL0 = IJFL(ILOW(IT)) + 1  (edge position + 1)
    //     set IJALI(IJFL0 - {1,2,3}) = 0  (3 points before edge)
    // Then CORRWM collects IJALI=0 points into IJFR.
    //
    // The Fortran selects frequencies near ionization edges of transitions
    // with IFC1 != 0. For the HHe LTE case, this gives 9 explicit points
    // at IJ=19,20,21 (He II edge) and 32-37 (H I/He I edges).
    //
    // Strategy: only mark frequencies near the most important ionization edges
    // (ground states of H I, He I, He II) as explicit. These are the edges
    // where the continuum opacity is most important for energy balance.
    // Fortran INIFRC(1) IJALI selection:
    // Mark frequencies near ionization edges (with IFC1 != 0) as explicit (IJALI=0).
    // For the H-He LTE case, the Fortran gives NFREQE=9 at indices 19,20,21,32-37.
    // These correspond to the top ionization edges: He II ground, He I ground,
    // He II N=2, and H I ground.
    let mut ijali = vec![1_i32; nfreq]; // 1 = ALI (default), 0 = explicit
    let top_edge_freqs: &[f64] = &frlev[..4.min(frlev.len())];
    for &edge_freq in top_edge_freqs {
        // Match Fortran's narrow window: only frequencies very close to the edge
        // The Fortran uses IFC1 transition flags to identify edge-adjacent points
        for ij in 0..nfreq {
            let fr = all_freqs[ij];
            let ratio = fr / edge_freq;
            // Tighter window to match Fortran's NFREQE=9 behavior
            if ratio > 0.95 && ratio < 1.05 {
                ijali[ij] = 0;
            }
        }
    }
    // CORRWM: collect explicit points (IJALI=0) into IJFR
    let ijfr: Vec<usize> = (0..nfreq).filter(|&ij| ijali[ij] == 0).collect();

    // Verify NFREQE <= MFREX
    let mut ijfr = ijfr;
    let nfreqe = ijfr.len();
    if nfreqe > crate::tlusty::state::constants::MFREX {
        eprintln!("WARNING: NFREQE={} > MFREX={}, truncating explicit frequencies", nfreqe, crate::tlusty::state::constants::MFREX);
        ijfr.truncate(crate::tlusty::state::constants::MFREX);
    }

    eprintln!("INIFRC grid: {} points, range [{:.4e}, {:.4e}], NFREQE={} explicit",
              nfreq, all_freqs[0], all_freqs[nfreq - 1], ijfr.len());

    LteFrequencyGrid { freq: all_freqs, weights: all_w, bnue, ijxco: all_ijxco, ijfr }
}

/// 计算 LTE 模式的完整不透明度。
pub fn lte_meanopt(params: &LteOpacityParams, grid: &LteFrequencyGrid) -> LteOpacityOutput {
    let t = params.t;
    let ne = params.ne;
    let nh = params.nh_neutral;
    let np = params.np;
    let nhm = params.nhm;
    let rho = params.rho;

    if rho <= 0.0 {
        return LteOpacityOutput {
            opros: 0.4,
            oppla: 0.4,
            opes: 0.0,
            opbf: 0.0,
            opff: 0.0,
            ophm: 0.0,
        };
    }

    let hkt = HK / t;
    let sqrt_t = t.sqrt();
    let sgff = SGFF0 / sqrt_t * ne;

    let mut abr = 0.0;
    let mut sumdb = 0.0;
    let mut abp = 0.0;
    let mut sumb = 0.0;

    for (ij, &fr) in grid.freq.iter().enumerate() {
        let w = grid.weights[ij];
        let bnue = grid.bnue[ij];

        let x = hkt * fr;
        let x_clamped = x.min(150.0);
        let ex = x_clamped.exp();
        let e1 = 1.0 / (ex - 1.0);

        // ∂B_ν/∂T·w = plan·u·ex·e1 (u=hkt·fr); the constant T it implicitly omits
        // cancels in the Rosseland ratio. Single e1 — matches faithful meanopt.rs
        // and Fortran tlusty208.f:22433 (DPLAN=PLAN*X/T/(UN-UN/EX)). A previous
        // `*e1*e1` here was the "κ_R 偏高 ~2-3x" compensation error noted at
        // main.rs:1573 — the extra frequency-dependent e1 re-weights the mean.
        let plan = bnue * e1 * w;
        let dplan = plan * hkt * fr * ex * e1;

        let (ab, sct) = compute_opacity_at_frequency(fr, t, ne, nh, np, nhm, hkt, sgff, params);

        let total = ab + sct;
        if total > 0.0 {
            abr += dplan / total;
        }
        sumdb += dplan;

        abp += plan * ab;
        sumb += plan;
    }

    let oprol = if abr > 0.0 { sumdb / abr } else { 0.0 };
    let opplal = if sumb > 0.0 { abp / sumb } else { 0.0 };

    let opros = oprol / rho;
    let oppla = opplal / rho;

    let opes = SIGE * ne / rho;
    let (opbf, opff, ophm) = compute_mean_opacities_per_gram(params, sqrt_t);

    LteOpacityOutput {
        opros,
        oppla,
        opes,
        opbf,
        opff,
        ophm,
    }
}

/// 计算给定频率点的吸收和散射系数 (per cm³)。
pub fn compute_opacity_at_frequency(
    fr: f64,
    t: f64,
    ne: f64,
    nh: f64,
    np: f64,
    nhm: f64,
    hkt: f64,
    sgff: f64,
    params: &LteOpacityParams,
) -> (f64, f64) {
    let mut ab = 0.0;
    let sct = SIGE * ne;

    // 1. 氢束缚-自由
    if fr >= FRH && nh > 0.0 {
        let sigma_bf0 = 6.3e-18;
        let sigma_bf = sigma_bf0 * (FRH / fr).powi(3);
        let gaunt_bf = hydrogen_gaunt_bf(fr);
        ab += sigma_bf * gaunt_bf * nh;
    }

    // 2. 氢自由-自由
    // 注意: 受激发射因子当前为 1/(1-e^-hν/kT). 诊断显示此式在高温深层使 Rosseland
    // 平均 κ_R 发散 (gold-ref 条件下 d69 κ_R≈140, 物理上应 ~1). 但简单改为乘以
    // (1-e^-hν/kT) 虽修正孤立 κ 值, 却因 κ-ρ-Ne-Saha 耦合使灰大气深度网格更差
    // (DM[69] 163→126, gold=298), 且 Fortran H- 自由-自由亦用除法 (tlusty208.f:11147).
    // 忠实修复需移植 Fortran SFF2/SFF3 表格化系数, 非简单因子翻转. 暂保留原式.
    // [2026-06-18 复核] 同时翻转 sf2 与改 bnue 为本地 T 仍非稳健: 灰大气 DM[69]
    // 163→216 (改善) 但 gold-ref 深层诊断 κ_R 140→500 (恶化), 单元测试 es_frac 失败.
    // ⇒ 简化 lte_meanopt 有相互补偿的误差, 局部物理修正会交换误差而非收敛.
    //     真正修复 = 移植 TLUSTY 完整 ROSSOP/COMOP 不透明度机制 (含 SFF2=EXP(FF·HK/T)
    //     约定, exact Gaunt, WOP 占据概率, H- SFFHMI 表). 暂保留原式.
    if np > 0.0 && ne > 0.0 {
        let frinv = 1.0 / fr;
        let fr3inv = frinv * frinv * frinv;

        let sf1 = sgff * fr3inv;
        let exp_factor = (-hkt * fr).exp();
        let sf2 = 1.0 / (1.0 - exp_factor).max(1e-30);
        let absoff = sf1 * sf2 * np;
        ab += absoff;
    }

    // 3. H- 自由-自由
    if nhm > 0.0 && ne > 0.0 {
        let frinv = 1.0 / fr;
        let cfft = CFF2 - CFF3 / t;
        let abhm_ff = (CFF1 + cfft * frinv) * nhm * ne * frinv;
        ab += abhm_ff;
    }

    // 4. H- 束缚-自由
    if nhm > 0.0 && fr >= FRHM {
        let sigma_hm = compute_hm_photodetachment_cross_section(fr);
        ab += sigma_hm * nhm;
    }

    // 5. He 束缚-自由
    if params.xhe > 0.0 {
        let he_abundance = params.xhe / 4.0 * params.nh_total / params.xh.max(0.1);
        if fr >= 1.81e15 && he_abundance > 0.0 {
            let sigma_he = 7.83e-18 * (1.81e15 / fr).powi(3);
            let he_neutral = he_abundance * 0.9;
            ab += sigma_he * he_neutral;
        }
    }

    (ab, sct)
}

/// 计算氢束缚-自由 Gaunt 因子。
fn hydrogen_gaunt_bf(fr: f64) -> f64 {
    let u = fr / FRH;
    if u < 1.0 {
        0.0
    } else if u < 2.0 {
        0.9
    } else if u < 10.0 {
        0.85
    } else {
        0.8
    }
}

/// 计算 H- 光致分离截面。
fn compute_hm_photodetachment_cross_section(fr: f64) -> f64 {
    if fr < FRHM {
        return 0.0;
    }

    let x = fr / FRHM - 1.0;
    if x <= 0.0 {
        return 0.0;
    }

    let sqrt_x = x.sqrt();
    let sigma_0 = 4.0e-17;
    let a = 1.0 + 0.5 * x - 0.1 * x * x;
    sigma_0 * sqrt_x * a
}

/// 计算平均不透明度分量 (每克)。
fn compute_mean_opacities_per_gram(params: &LteOpacityParams, _sqrt_t: f64) -> (f64, f64, f64) {
    let rho = params.rho;
    if rho <= 0.0 {
        return (0.0, 0.0, 0.0);
    }

    let t = params.t;
    let t4 = t / 1e4;
    let t_factor = t4.powf(-3.5);

    let ionization = if params.nh_total > 0.0 {
        (params.np / params.nh_total).min(1.0)
    } else {
        1.0
    };

    let kappa_bf_h = 4.3e-25 * (1.0 - ionization) * t_factor * params.xh;
    let kappa_bf_he = 1.0e-25 * (1.0 - ionization) * t_factor * params.xhe;
    let opbf = kappa_bf_h + kappa_bf_he;

    let kappa_ff = 1.0e-26 * ionization * (1.0 + ionization) * t_factor;
    let opff = kappa_ff;

    let ophm = if params.nhm > 0.0 && t < 10000.0 {
        let t4_inv = 1e4 / t;
        let sigma_hm = 4e-17;
        sigma_hm * params.nhm / rho * t4_inv * t4_inv
    } else {
        0.0
    };

    (opbf, opff, ophm)
}

/// 快速计算 LTE Rosseland 平均不透明度（解析近似）。
pub fn quick_lte_rosseland(params: &LteOpacityParams) -> f64 {
    let rho = params.rho;
    if rho <= 0.0 {
        return 0.4;
    }

    let t = params.t;
    let ne = params.ne;
    let np = params.np;
    let nh_neutral = params.nh_neutral;

    let kappa_es = SIGE * ne / rho;

    let t4 = t / 1e4;
    let t_factor = t4.powf(-3.5);

    let nh_total = np + nh_neutral;
    let ionization = if nh_total > 0.0 {
        (np / nh_total).min(1.0)
    } else {
        1.0
    };

    let kramer_bf = 4.3e-25 * (1.0 - ionization) * t_factor;
    let kramer_ff = 1.0e-26 * ionization * (1.0 + ionization) * t_factor;

    let nh_factor = nh_total / rho.max(1e-30);

    kappa_es + (kramer_bf + kramer_ff) * nh_factor
}

// ============================================================================
// 测试
// ============================================================================

#[cfg(test)]
mod tests {
    use super::*;

    /// Diagnostic: compute LTE Rosseland opacity breakdown for gold-ref (T,Ne,ρ)
    /// profile points, compare to effective κ = tau/DM from the converged grid.
    /// Purpose: find which opacity source is overestimated at depth (grey-start
    /// grid compressed because κ_rust ≈ 3× too high at depth vs gold κ≈1.06).
    #[test]
    fn diag_goldref_opacity_breakdown() {
        // (label, T, Ne, rho, eff_kappa=tau/DM) from tests/tlusty/hhe_fortran/fort.7.ref
        let pts: &[(&str, f64, f64, f64, f64)] = &[
            ("d0  surf", 26306.2, 3.764e8,  7.304e-16, 0.343),
            ("d20      ", 27030.2, 2.258e11, 4.455e-13, 0.343),
            ("d34      ", 27800.0, 5.0e12,   1.0e-11,   0.396),
            ("d49      ", 40000.0, 1.0e14,   2.0e-10,   0.951),
            ("d60      ", 90000.0, 2.0e15,   4.0e-9,    1.145),
            ("d69 deep ", 137872.1, 5.679e16, 1.102e-7, 1.061),
        ];
        let wmm = 1.3 * 1.67e-24; // mean molecular weight
        let grid = generate_lte_frequency_grid(35000.0, 200);
        eprintln!("\n{:>9} {:>10} {:>10} {:>10} {:>10} {:>10} | {:>8}",
            "label","kappa_R","opes","opff","opbf","ophm","eff_k");
        for (label, t, ne, rho, eff_k) in pts {
            // H fully ionized at these T: np ~ n_H, neutral H tiny
            let n_heavy = rho / wmm;
            let nh_total = 0.70 * n_heavy * 2.0; // X=0.70 fraction, nucleon count
            let np = nh_total * 0.999;
            let nh_neutral = nh_total * 0.001;
            let params = LteOpacityParams {
                t: *t, ne: *ne, nh_total, np, nh_neutral, nhm: 0.0, rho: *rho,
                uh: 2.0, uhe: 1.0, uhep: 2.0, xh: 0.70, xhe: 0.28,
            };
            let r = lte_meanopt(&params, &grid);
            eprintln!("{:>9} {:10.3} {:10.3} {:10.3} {:10.3} {:10.3} | {:8.3}",
                label, r.opros, r.opes, r.opff, r.opbf, r.ophm, eff_k);
        }
    }

    #[test]
    fn test_lte_opacity_hot_star() {
        let params = LteOpacityParams {
            t: 30000.0,
            ne: 1e14,
            nh_total: 1e14,
            np: 9e13,
            nh_neutral: 1e13,
            nhm: 0.0,
            rho: 1e-10,
            uh: 2.0,
            uhe: 1.0,
            uhep: 2.0,
            xh: 0.70,
            xhe: 0.28,
        };

        let grid = generate_lte_frequency_grid(35000.0, 100);
        let result = lte_meanopt(&params, &grid);

        assert!(result.opros > 0.0);
        assert!(result.opes / result.opros > 0.3);
    }

    #[test]
    fn test_quick_lte_rosseland() {
        let params = LteOpacityParams {
            t: 10000.0,
            ne: 1e13,
            nh_total: 1e15,
            np: 5e12,
            nh_neutral: 5e14,
            nhm: 0.0,
            rho: 1e-10,
            ..Default::default()
        };

        let kappar = quick_lte_rosseland(&params);
        assert!(kappar > 0.0);
    }
}