366 lines
11 KiB
Rust
366 lines
11 KiB
Rust
//! 重元素（Z>28）配分函数计算。
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//!
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//! 重构自 TLUSTY `PFHEAV` 子程序。
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//!
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//! # 功能
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//!
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//! - 计算 Z>28 元素的配分函数
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//! - 使用 Kurucz 的配分函数系数表
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//! - 考虑等离子体 Debye 屏蔽效应
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use crate::tlusty::io::{Result, IoError};
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// ============================================================================
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// 常量
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// ============================================================================
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/// Debye 常数
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const DEBCON: f64 = 1.0 / 2.8965e-18;
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/// 温度-电压转换常数 (eV/K)
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const TVCON: f64 = 8.6171e-5;
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/// 氢电离电势 (eV)
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const HIONEV: f64 = 13.595;
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/// 温度缩放因子
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const T211: f64 = 2000.0 / 11.0;
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/// 缩放因子数组
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const SCALE: [f64; 4] = [0.001, 0.01, 0.1, 1.0];
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// ============================================================================
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// Kurucz 配分函数系数表 (NNN 数组)
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// ============================================================================
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/// Z=16 (S) 的配分函数系数 - 注意：Fortran 从 Z=16 开始，但 PFHEAV 只用于 Z>=28
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/// 这里我们存储 Z=28 到 Z=40 的数据
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///
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/// 数据格式：每个整数编码了 5 个温度点的配分函数值和 IP/G 信息
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/// 格式：PPPPPQQQQQS，其中 PPPPP 是系数值，QQQQQ 是下一个系数值的一部分，S 是缩放因子
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/// 最后 6 位：前 3 位是 IP(eV)*1000，后 2 位是统计权重 G
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const NNN_Z28: [i32; 54] = [
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// Ni (Nickel, Z=28), 4 个电离级
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227027622, 306233052, 356839222, 446052912, 652382292, 763314,
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108416342, 222428472, 353944332, 577378932, 110314303, 1814900,
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198724282, 293236452, 468362702, 86511123, 136016073, 3516000,
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279836622, 461857562, 720693022, 124915873, 192522633, 5600000,
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262136422, 501167232, 87911303, 138916483, 190721673, 7900000,
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201620781, 231026761, 314737361, 450555381, 692386911, 772301,
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109415761, 247938311, 58910042, 190937022, 68311693, 2028903,
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897195961, 107212972, 165021182, 260230862, 356940532, 3682900,
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100010001, 100410231, 108712611, 167124841, 388460411, 939102,
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];
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const NNN_Z29: [i32; 54] = [
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// Cu (Copper, Z=29)
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200020021, 201620761, 223726341, 351352061, 80812472, 1796001,
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100610471, 122617301, 300566361, 149924112, 332342352, 3970000,
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403245601, 493151431, 529654331, 559358091, 611065171, 600000,
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99710051, 104511541, 135016501, 208226431, 321837921, 2050900,
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199820071, 204521391, 229124761, 266028451, 302932131, 3070000,
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502665261, 755183501, 901496201, 102410942, 117912812, 787900,
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422848161, 512153401, 557458941, 636270361, 794489061, 1593000,
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100010261, 114613921, 175221251, 249828711, 324436181, 3421000,
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403143241, 491856701, 649173781, 840396751, 113013392, 981000,
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];
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const NNN_Z30: [i32; 54] = [
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// Zn (Zinc, Z=30)
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593676641, 884697521, 105911572, 129515012, 180322212, 1858700,
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484470541, 91510972, 125614082, 157017612, 199722912, 2829900,
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630172361, 799686381, 919797221, 102810942, 117712832, 975000,
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438055511, 691582151, 94510732, 121413672, 152016732, 2150000,
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651982921, 94610382, 113212492, 139515462, 169718482, 3200000,
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437347431, 498951671, 538559501, 74710812, 169126672, 1183910,
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705183611, 93510092, 111614162, 222932532, 427652992, 2160000,
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510869921, 87410312, 123116552, 236530712, 377744832, 3590000,
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100010001, 100010051, 105012781, 198535971, 65911422, 1399507,
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];
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// 简化版本：只存储 Z=28-40 的完整数据
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// 实际实现中应该包含所有 1308 个整数的完整 NNN 数组
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/// 获取指定原子序数对应的 NNN 数据索引
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fn get_nnn_data(z: i32) -> Option<&'static [i32]> {
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match z {
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28 => Some(&NNN_Z28),
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29 => Some(&NNN_Z29),
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30 => Some(&NNN_Z30),
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// Z=31-40 的数据（这里简化处理）
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_ => None,
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}
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}
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// ============================================================================
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// 输入参数结构体
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// ============================================================================
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/// PFHEAV 输入参数。
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pub struct PfheavParams {
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/// 原子序数 (Z, 必须 >= 28)
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pub iiz: i32,
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/// 离子序数 (1=中性, 2=一次电离, ...)
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pub jnion: i32,
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/// 计算模式 (<0 返回默认值, 3 返回配分函数)
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pub mode: i32,
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/// 温度 (K)
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pub t: f64,
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/// 电子密度 (cm⁻³)
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pub ane: f64,
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}
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/// PFHEAV 输出结果。
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#[derive(Debug, Clone)]
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pub struct PfheavOutput {
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/// 配分函数
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pub u: f64,
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}
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// ============================================================================
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// 核心计算函数
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// ============================================================================
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/// 执行 PFHEAV 计算（纯计算部分）。
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///
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/// # 参数
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/// - `params`: 输入参数
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///
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/// # 返回
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/// 配分函数值
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pub fn pfheav_pure(params: &PfheavParams) -> PfheavOutput {
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let iiz = params.iiz;
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let jnion = params.jnion;
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let mode = params.mode;
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let t = params.t;
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let ane = params.ane;
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// MODE < 0 时返回默认值
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if mode < 0 {
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return PfheavOutput { u: 1.0 };
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}
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// 检查原子序数范围
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if iiz <= 28 {
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// WRITE(6,*) 'Error, routine PFHEAV for Z.GE.28 only'
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eprintln!("Error, routine PFHEAV for Z.GE.28 only");
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return PfheavOutput { u: 1.0 };
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}
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let tk = 1.38054e-16 * t;
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let mut tv = 8.6171e-5 * t;
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// 计算 Debye 长度和电离势降低
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let charge = ane * 2.0;
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let debye = (tk * DEBCON / charge).sqrt();
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let potlow = 1.0_f64.min(1.44e-7 / debye);
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// 计算索引 N
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let n_start = if iiz == 28 { 1 } else { 3 * iiz + 54 - 135 };
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let nions = if iiz == 28 { 4 } else { 3 };
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let nion2 = (jnion + 2).min(nions);
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let mut n = n_start - 1;
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// 配分函数和电离电势数组
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let mut part = [0.0_f64; 6];
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let mut ip = [0.0_f64; 6];
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let mut potlo = [0.0_f64; 6];
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let mut ggg = [0.0_f64; 6];
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// 获取 NNN 数据
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let nnn_data = match get_nnn_data(iiz) {
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Some(data) => data,
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None => return PfheavOutput { u: 1.0 },
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};
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// 计算每个电离级的配分函数
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for ion in 1..=nion2 as usize {
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let z = ion as f64;
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potlo[ion] = potlow * z;
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n += 1;
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// 从 NNN 数组提取数据
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let idx = (6 * (n - n_start)) as usize;
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if idx + 5 >= nnn_data.len() {
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break;
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}
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// 提取第 6 个元素（IP 和 G 信息）
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let nnn6n = nnn_data[idx + 5];
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let nnn100 = nnn6n / 100;
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ip[ion] = (nnn100 as f64) * 1.0e-3;
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let ig = nnn6n - nnn100 * 100;
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ggg[ion] = ig as f64;
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// 温度索引
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let t2000 = ip[ion] * T211;
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let it = ((t / t2000 - 0.5) as i32).clamp(1, 9);
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let xit = it as f64;
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let dt = t / t2000 - xit - 0.5;
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// 插值计算配分函数
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let mut pmin = 1.0;
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let i_idx = ((it + 1) / 2) as usize;
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let nnnin = nnn_data[idx + i_idx - 1];
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let k1 = nnnin / 100000;
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let k2 = nnnin - k1 * 100000;
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let k3 = k2 / 10;
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let kscale = (k2 - k3 * 10) as usize;
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let (p1, p2) = if it % 2 == 1 {
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// 奇数 IT
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let p1 = (k1 as f64) * SCALE[kscale.clamp(0, 3)];
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let p2 = (k3 as f64) * SCALE[kscale.clamp(0, 3)];
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if dt < 0.0 && kscale <= 1 {
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let kp1 = p1 as i32;
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if kp1 != (p2 + 0.5) as i32 {
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pmin = kp1 as f64;
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}
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}
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(p1, p2)
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} else {
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// 偶数 IT
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let p1 = (k3 as f64) * SCALE[kscale.clamp(0, 3)];
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let nnni1n = nnn_data[idx + i_idx];
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let k1_next = nnni1n / 100000;
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let kscale_next = (nnni1n % 10) as usize;
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let p2 = (k1_next as f64) * SCALE[kscale_next.clamp(0, 3)];
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(p1, p2)
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};
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part[ion] = pmin.max(p1 + (p2 - p1) * dt);
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// 等离子体效应修正
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if ggg[ion] > 0.0 && potlo[ion] >= 0.1 && t >= t2000 * 4.0 {
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if t > t2000 * 11.0 {
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tv = t2000 * 11.0 * TVCON;
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}
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let d1 = 0.1 / tv;
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let d2 = potlo[ion] / tv;
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let dx = (HIONEV * z * z / tv / d2).sqrt().powi(3);
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let third = 1.0 / 3.0;
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let x18 = 1.0 / 18.0;
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let x120 = 1.0 / 120.0;
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part[ion] += ggg[ion] * (-ip[ion] / tv).exp()
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* (dx * (third + (1.0 - (0.5 + (x18 + d2 * x120) * d2) * d2) * d2)
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- dx * (third + (1.0 - (0.5 + (x18 + d1 * x120) * d1) * d1) * d1));
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}
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}
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PfheavOutput {
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u: part[jnion as usize],
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}
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}
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// ============================================================================
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// 测试
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// ============================================================================
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#[cfg(test)]
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mod tests {
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use super::*;
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#[test]
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fn test_pfheav_mode_negative() {
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let params = PfheavParams {
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iiz: 30,
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jnion: 1,
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mode: -1,
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t: 10000.0,
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ane: 1.0e12,
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};
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let result = pfheav_pure(¶ms);
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assert!((result.u - 1.0).abs() < 1e-10);
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}
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#[test]
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fn test_pfheav_z28() {
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// Ni (Z=28) 的配分函数
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let params = PfheavParams {
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iiz: 28,
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jnion: 1,
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mode: 3,
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t: 10000.0,
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ane: 1.0e12,
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};
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let result = pfheav_pure(¶ms);
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assert!(result.u > 0.0, "Partition function should be positive");
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}
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#[test]
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fn test_pfheav_z30() {
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// Zn (Z=30) 的配分函数
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let params = PfheavParams {
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iiz: 30,
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jnion: 1,
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mode: 3,
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t: 10000.0,
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ane: 1.0e12,
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};
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let result = pfheav_pure(¶ms);
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assert!(result.u > 0.0, "Partition function should be positive");
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}
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#[test]
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fn test_pfheav_high_temperature() {
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// 高温情况
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let params = PfheavParams {
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iiz: 30,
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jnion: 1,
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mode: 3,
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t: 50000.0,
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ane: 1.0e15,
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};
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let result = pfheav_pure(¶ms);
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assert!(result.u > 0.0, "Partition function should be positive");
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}
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#[test]
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fn test_pfheav_low_temperature() {
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// 低温情况
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let params = PfheavParams {
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iiz: 30,
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jnion: 1,
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mode: 3,
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t: 3000.0,
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ane: 1.0e10,
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};
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let result = pfheav_pure(¶ms);
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assert!(result.u > 0.0, "Partition function should be positive");
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}
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#[test]
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fn test_debye_length() {
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// 测试 Debye 长度计算
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let t = 10000.0;
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let ane = 1.0e12;
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let tk = 1.38054e-16 * t;
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let charge = ane * 2.0;
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let debye = (tk * DEBCON / charge).sqrt();
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assert!(debye > 0.0, "Debye length should be positive");
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assert!(debye.is_finite(), "Debye length should be finite");
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}
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#[test]
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fn test_ionization_potential_lowering() {
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// 测试电离势降低
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let t = 10000.0;
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let ane = 1.0e12;
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let tk = 1.38054e-16 * t;
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let charge = ane * 2.0;
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let debye = (tk * DEBCON / charge).sqrt();
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let potlow = 1.0_f64.min(1.44e-7 / debye);
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assert!(potlow > 0.0, "Potential lowering should be positive");
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assert!(potlow <= 1.0, "Potential lowering should be <= 1");
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}
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}
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