SpectraRust/src/math/starka.rs

//! 氢线 Stark 展宽近似表达式。
//!
//! 重构自 TLUSTY `starka.f`。
//!
//! 当温度或电子密度超出 Lemke 表格范围时，使用近似表达式计算氢线 Stark 轮廓。

// ============================================================================
// 常量参数
// ============================================================================

const F0: f64 = -0.5758228;
const F1: f64 = 0.4796232;
const F2: f64 = 0.07209481;
const AL: f64 = 1.26;

const SD: f64 = 0.5641895;
const SLO: f64 = -2.5;
const THRA: f64 = 1.5;
const BL1: f64 = 1.14;
const BL2: f64 = 11.4;

const SAC: f64 = 0.08;
const PISQ1: f64 = 1.0 / 1.77245385090551; // 1 / sqrt(pi)

// ============================================================================
// STARKA - Stark 展宽近似表达式
// ============================================================================

/// 计算氢线 Stark 展宽的近似表达式。
///
/// 当温度或电子密度超出 Lemke 表格范围时使用。
///
/// # 参数
///
/// - `beta` - 以 β 单位表示的波长位移 (Δλ/β)
/// - `fac` - 乘法因子 (H I 为 2.0，He II 为 1.0)
/// - `adh` - 辅助参数 A = 1.5*ln(BETAD) - 1.761
/// - `betad` - 以 β 单位表示的 Doppler 宽度
/// - `divh` - Doppler 核心与 Stark 翼的分界点 (以 betad 为单位)
///
/// # 返回
///
/// Stark 轮廓值 S(β)
///
/// # Fortran 原始代码
///
/// ```fortran
/// FUNCTION STARKA(BETA,FAC)
///   ...
///   BETAD1=UN/BETAD
///   IF(ADH.GT.AL) THEN
///      XD=BETA*BETAD1
///      IF(XD.LE.DIVH) THEN
///         STARKA=EXP(-XD*XD)*BETAD1*PISQ1
///       ELSE
///         STARKA=THRA*FAC*EXP(SLO*LOG(BETA))
///      END IF
///    ELSE
///      IF(BETA.LE.BL1) THEN
///         STARKA=SAC
///       ELSE IF(BETA.LT.BL2) THEN
///         XL=LOG(BETA)
///         FL=(F0*XL+F1)*XL
///         STARKA=F2*EXP(FL)
///       ELSE
///         STARKA=THRA*FAC*EXP(SLO*LOG(BETA))
///      END IF
///   END IF
/// END
/// ```
pub fn starka(beta: f64, fac: f64, adh: f64, betad: f64, divh: f64) -> f64 {
    let betad1 = 1.0 / betad;

    if adh > AL {
        // a > 1: Doppler 核心 + 渐近 Holtsmark 翼
        let xd = beta * betad1;
        if xd <= divh {
            // Doppler 核心
            (-xd * xd).exp() * betad1 * PISQ1
        } else {
            // 渐近 Holtsmark 翼
            THRA * fac * beta.powf(SLO)
        }
    } else {
        // a < 1: 经验公式
        if beta <= BL1 {
            SAC
        } else if beta < BL2 {
            let xl = beta.ln();
            let fl = (F0 * xl + F1) * xl;
            F2 * fl.exp()
        } else {
            THRA * fac * beta.powf(SLO)
        }
    }
}

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

    #[test]
    fn test_starka_doppler_core() {
        // a > 1, xd <= divh: Doppler 核心
        let adh = 2.0; // > AL = 1.26
        let betad = 10.0;
        let divh = 5.0;
        let beta = 30.0; // xd = 30/10 = 3 <= 5

        let result = starka(beta, 2.0, adh, betad, divh);

        // 应该是 Doppler 核心值
        let xd = beta / betad;
        let expected = (-xd * xd).exp() / betad * PISQ1;
        assert!((result - expected).abs() < 1e-10);
    }

    #[test]
    fn test_starka_holtsmark_wing() {
        // a > 1, xd > divh: Holtsmark 翼
        let adh = 2.0;
        let betad = 10.0;
        let divh = 5.0;
        let beta = 100.0; // xd = 100/10 = 10 > 5

        let result = starka(beta, 2.0, adh, betad, divh);

        // 应该是 Holtsmark 翼值
        let expected = THRA * 2.0 * beta.powf(SLO);
        assert!((result - expected).abs() < 1e-10);
    }

    #[test]
    fn test_starka_empirical_low_beta() {
        // a <= 1, beta <= BL1
        let adh = 0.5; // < AL
        let result = starka(0.5, 2.0, adh, 10.0, 5.0);
        assert!((result - SAC).abs() < 1e-10);
    }

    #[test]
    fn test_starka_empirical_mid_beta() {
        // a <= 1, BL1 < beta < BL2
        let adh = 0.5;
        let beta = 5.0; // 1.14 < 5.0 < 11.4
        let result = starka(beta, 2.0, adh, 10.0, 5.0);

        let xl = beta.ln();
        let fl = (F0 * xl + F1) * xl;
        let expected = F2 * fl.exp();
        assert!((result - expected).abs() < 1e-10);
    }

    #[test]
    fn test_starka_empirical_high_beta() {
        // a <= 1, beta >= BL2
        let adh = 0.5;
        let beta = 20.0; // > 11.4
        let result = starka(beta, 2.0, adh, 10.0, 5.0);

        let expected = THRA * 2.0 * beta.powf(SLO);
        assert!((result - expected).abs() < 1e-10);
    }

    #[test]
    fn test_starka_factor_difference() {
        // 测试不同 fac 值的影响
        let adh = 2.0;
        let betad = 10.0;
        let divh = 5.0;
        let beta = 100.0;

        let result_hi = starka(beta, 2.0, adh, betad, divh);
        let result_he = starka(beta, 1.0, adh, betad, divh);

        // fac 越大，结果越大
        assert!(result_hi > result_he);
        assert!((result_hi / result_he - 2.0).abs() < 1e-10);
    }
}