AIDT 온디바이스 STEM 공명 비탄성 X선 산란(RIXS) 크라머스-하이젠베르크 매그논 서보 엔진

using System;
using System.Runtime.CompilerServices;

namespace ZeliDesk.Stem.Rixs
{
    public readonly ref struct RixsScanState
    {
        public readonly double MomentumTransferQx;  // 역격자 전송 운동량 q_x (pi/a 단위)
        public readonly double EnergyLossEv;        // 에너지 손실 hw (eV)
        public readonly double MagnonEnergyMev;     // 이론 매그논 분산 에너지 (meV)
        public readonly double ScatteringIntensity; // 정규화 RIXS 피크 강도
        public readonly double CoreHoleLifetimeFs;  // 중간상 코어홀 수명 (fs)
        public readonly double SpectrometerAngleDeg; // 분광기 회전각 2-theta (deg)

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public RixsScanState(double qx, double eloss, double magnonMev, double intensity, double lifeFs, double angleDeg)
        {
            MomentumTransferQx = qx;
            EnergyLossEv = eloss;
            MagnonEnergyMev = magnonMev;
            ScatteringIntensity = intensity;
            CoreHoleLifetimeFs = lifeFs;
            SpectrometerAngleDeg = angleDeg;
        }
    }

    public ref struct RixsSpectrometerEngine
    {
        private const double HBar = 1.054571817e-34;   // J*s
        private const double C = 299792458.0;
        private const double ECharge = 1.602176634e-19; // C
        private const double CuL3EdgeEv = 931.5;        // Cu L3-edge (eV)

        private readonly double _exchangeJJoules;       // 스핀 교환 계수 J (J)
        private readonly double _latticeConstantA;      // 격자 상수 a (m, 3.8 Angstrom)
        private double _incidentEnergyEv;               // 입사 광자 에너지 (eV)
        private double _sampleThetaDeg;                 // 시료 입사각 (deg)

        public RixsSpectrometerEngine(double jMev = 130.0, double latticeAngstrom = 3.8)
        {
            _exchangeJJoules = jMev * 1e-3 * ECharge;
            _latticeConstantA = latticeAngstrom * 1e-10;
            _incidentEnergyEv = CuL3EdgeEv; // 공명 조건
            _sampleThetaDeg = 20.0;
        }

        [MethodImpl(MethodImplOptions.AggressiveInlining)]
        public RixsScanState StepServo(double targetQxPiA, double thetaStepDeg, double dtSec)
        {
            _sampleThetaDeg += thetaStepDeg;

            // 1. 입사 및 산란 X선 파수 k_i 계산
            double kMeters = (_incidentEnergyEv * ECharge) / (HBar * C);

            // 2. 평면 내 전송 운동량 q_x 계산 (pi/a 단위 정규화)
            double twoThetaDeg = 130.0; // 고정된 분광기 산란각 130도 가정
            double qMeters = kMeters * (Math.Cos((twoThetaDeg - _sampleThetaDeg) * Math.PI / 180.0) - Math.Cos(_sampleThetaDeg * Math.PI / 180.0));
            double qxNorm = qMeters * _latticeConstantA / Math.PI;

            // 3. 2D 반강자성 하이젠베르크 모델 매그논 분산 계산
            // hbar*omega(q) = 2 * J * Zc * sqrt(1 - gamma_q^2) where gamma_q = 0.5 * (cos(qx*pi) + 1) for qy=0
            double gammaQ = 0.5 * (Math.Cos(Math.Clamp(qxNorm, -1.0, 1.0) * Math.PI) + 1.0);
            double magnonDispersionJoules = 2.0 * _exchangeJJoules * 1.18 * Math.Sqrt(Math.Max(1.0 - gammaQ * gammaQ, 0.001));
            double magnonEnergyMev = (magnonDispersionJoules / ECharge) * 1000.0;

            // 4. 크라머스-하이젠베르크 코어홀(Gamma = 0.3 eV) 로렌츠 공명 강도 모델
            double coreHoleWidthEv = 0.30; // 300 meV
            double coreHoleLifeFs = (HBar / (coreHoleWidthEv * ECharge)) * 1e15;
            double detuning = _incidentEnergyEv - CuL3EdgeEv;
            double resonanceFactor = 1.0 / (detuning * detuning + (coreHoleWidthEv * 0.5) * (coreHoleWidthEv * 0.5));
            double intensity = resonanceFactor * (1.0 - gammaQ);

            return new RixsScanState(
                qx: qxNorm,
                eloss: magnonEnergyMev * 1e-3,
                magnonMev: magnonEnergyMev,
                intensity: intensity,
                lifeFs: coreHoleLifeFs,
                angleDeg: twoThetaDeg
            );
        }
    }
}