[831] | 1 | // |
---|
| 2 | // ******************************************************************** |
---|
| 3 | // * License and Disclaimer * |
---|
| 4 | // * * |
---|
| 5 | // * The Geant4 software is copyright of the Copyright Holders of * |
---|
| 6 | // * the Geant4 Collaboration. It is provided under the terms and * |
---|
| 7 | // * conditions of the Geant4 Software License, included in the file * |
---|
| 8 | // * LICENSE and available at http://cern.ch/geant4/license . These * |
---|
| 9 | // * include a list of copyright holders. * |
---|
| 10 | // * * |
---|
| 11 | // * Neither the authors of this software system, nor their employing * |
---|
| 12 | // * institutes,nor the agencies providing financial support for this * |
---|
| 13 | // * work make any representation or warranty, express or implied, * |
---|
| 14 | // * regarding this software system or assume any liability for its * |
---|
| 15 | // * use. Please see the license in the file LICENSE and URL above * |
---|
| 16 | // * for the full disclaimer and the limitation of liability. * |
---|
| 17 | // * * |
---|
| 18 | // * This code implementation is the result of the scientific and * |
---|
| 19 | // * technical work of the GEANT4 collaboration. * |
---|
| 20 | // * By using, copying, modifying or distributing the software (or * |
---|
| 21 | // * any work based on the software) you agree to acknowledge its * |
---|
| 22 | // * use in resulting scientific publications, and indicate your * |
---|
| 23 | // * acceptance of all terms of the Geant4 Software license. * |
---|
| 24 | // ******************************************************************** |
---|
| 25 | // |
---|
| 26 | // |
---|
| 27 | // $Id: G4MagHelicalStepper.cc,v 1.23 2007/09/05 12:20:17 gcosmo Exp $ |
---|
[921] | 28 | // GEANT4 tag $Name: geant4-09-02-cand-01 $ |
---|
[831] | 29 | // |
---|
| 30 | // -------------------------------------------------------------------- |
---|
| 31 | |
---|
| 32 | #include "G4MagHelicalStepper.hh" |
---|
| 33 | #include "G4LineSection.hh" |
---|
| 34 | #include "G4Mag_EqRhs.hh" |
---|
| 35 | |
---|
| 36 | // given a purely magnetic field a better approach than adding a straight line |
---|
| 37 | // (as in the normal runge-kutta-methods) is to add helix segments to the |
---|
| 38 | // current position |
---|
| 39 | |
---|
| 40 | |
---|
| 41 | // Constant for determining unit conversion when using normal as integrand. |
---|
| 42 | // |
---|
| 43 | const G4double G4MagHelicalStepper::fUnitConstant = 0.299792458*(GeV/(tesla*m)); |
---|
| 44 | |
---|
| 45 | |
---|
| 46 | G4MagHelicalStepper::G4MagHelicalStepper(G4Mag_EqRhs *EqRhs) |
---|
| 47 | : G4MagIntegratorStepper(EqRhs, 6) // integrate over 6 variables only !! |
---|
| 48 | // position & velocity |
---|
| 49 | { |
---|
| 50 | fPtrMagEqOfMot = EqRhs; |
---|
| 51 | } |
---|
| 52 | |
---|
| 53 | G4MagHelicalStepper::~G4MagHelicalStepper() |
---|
| 54 | { |
---|
| 55 | } |
---|
| 56 | |
---|
| 57 | void |
---|
| 58 | G4MagHelicalStepper::AdvanceHelix( const G4double yIn[], |
---|
| 59 | G4ThreeVector Bfld, |
---|
| 60 | G4double h, |
---|
| 61 | G4double yHelix[], |
---|
| 62 | G4double yHelix2[] ) |
---|
| 63 | { |
---|
| 64 | // const G4int nvar = 6; |
---|
| 65 | |
---|
| 66 | // OLD const G4double approc_limit = 0.05; |
---|
| 67 | // OLD approc_limit = 0.05 gives max.error=x^5/5!=(0.05)^5/5!=2.6*e-9 |
---|
| 68 | // NEW approc_limit = 0.005 gives max.error=x^5/5!=2.6*e-14 |
---|
| 69 | |
---|
| 70 | const G4double approc_limit = 0.005; |
---|
| 71 | G4ThreeVector Bnorm, B_x_P, vperp, vpar; |
---|
| 72 | |
---|
| 73 | G4double B_d_P; |
---|
| 74 | G4double B_v_P; |
---|
| 75 | G4double Theta; |
---|
| 76 | G4double R_1; |
---|
| 77 | G4double R_Helix; |
---|
| 78 | G4double CosT2, SinT2, CosT, SinT; |
---|
| 79 | G4ThreeVector positionMove, endTangent; |
---|
| 80 | |
---|
| 81 | G4double Bmag = Bfld.mag(); |
---|
| 82 | const G4double *pIn = yIn+3; |
---|
| 83 | G4ThreeVector initVelocity= G4ThreeVector( pIn[0], pIn[1], pIn[2]); |
---|
| 84 | G4double velocityVal = initVelocity.mag(); |
---|
| 85 | G4ThreeVector initTangent = (1.0/velocityVal) * initVelocity; |
---|
| 86 | |
---|
| 87 | R_1=GetInverseCurve(velocityVal,Bmag); |
---|
| 88 | |
---|
| 89 | // for too small magnetic fields there is no curvature |
---|
| 90 | // (include momentum here) FIXME |
---|
| 91 | |
---|
| 92 | if( (std::fabs(R_1) < 1e-10)||(Bmag<1e-12) ) |
---|
| 93 | { |
---|
| 94 | LinearStep( yIn, h, yHelix ); |
---|
| 95 | |
---|
| 96 | // Store and/or calculate parameters for chord distance |
---|
| 97 | |
---|
| 98 | SetAngCurve(1.); |
---|
| 99 | SetCurve(h); |
---|
| 100 | SetRadHelix(0.); |
---|
| 101 | } |
---|
| 102 | else |
---|
| 103 | { |
---|
| 104 | Bnorm = (1.0/Bmag)*Bfld; |
---|
| 105 | |
---|
| 106 | // calculate the direction of the force |
---|
| 107 | |
---|
| 108 | B_x_P = Bnorm.cross(initTangent); |
---|
| 109 | |
---|
| 110 | // parallel and perp vectors |
---|
| 111 | |
---|
| 112 | B_d_P = Bnorm.dot(initTangent); // this is the fraction of P parallel to B |
---|
| 113 | |
---|
| 114 | vpar = B_d_P * Bnorm; // the component parallel to B |
---|
| 115 | vperp= initTangent - vpar; // the component perpendicular to B |
---|
| 116 | |
---|
| 117 | B_v_P = std::sqrt( 1 - B_d_P * B_d_P); // Fraction of P perp to B |
---|
| 118 | |
---|
| 119 | // calculate the stepping angle |
---|
| 120 | |
---|
| 121 | Theta = R_1 * h; // * B_v_P; |
---|
| 122 | |
---|
| 123 | // Trigonometrix |
---|
| 124 | |
---|
| 125 | if( std::fabs(Theta) > approc_limit ) |
---|
| 126 | { |
---|
| 127 | SinT = std::sin(Theta); |
---|
| 128 | CosT = std::cos(Theta); |
---|
| 129 | } |
---|
| 130 | else |
---|
| 131 | { |
---|
| 132 | G4double Theta2 = Theta*Theta; |
---|
| 133 | G4double Theta3 = Theta2 * Theta; |
---|
| 134 | G4double Theta4 = Theta2 * Theta2; |
---|
| 135 | SinT = Theta - 1.0/6.0 * Theta3; |
---|
| 136 | CosT = 1 - 0.5 * Theta2 + 1.0/24.0 * Theta4; |
---|
| 137 | } |
---|
| 138 | |
---|
| 139 | // the actual "rotation" |
---|
| 140 | |
---|
| 141 | G4double R = 1.0 / R_1; |
---|
| 142 | |
---|
| 143 | positionMove = R * ( SinT * vperp + (1-CosT) * B_x_P) + h * vpar; |
---|
| 144 | endTangent = CosT * vperp + SinT * B_x_P + vpar; |
---|
| 145 | |
---|
| 146 | // Store the resulting position and tangent |
---|
| 147 | |
---|
| 148 | yHelix[0] = yIn[0] + positionMove.x(); |
---|
| 149 | yHelix[1] = yIn[1] + positionMove.y(); |
---|
| 150 | yHelix[2] = yIn[2] + positionMove.z(); |
---|
| 151 | yHelix[3] = velocityVal * endTangent.x(); |
---|
| 152 | yHelix[4] = velocityVal * endTangent.y(); |
---|
| 153 | yHelix[5] = velocityVal * endTangent.z(); |
---|
| 154 | |
---|
| 155 | // Store 2*h step Helix if exist |
---|
| 156 | |
---|
| 157 | if(yHelix2) |
---|
| 158 | { |
---|
| 159 | SinT2 = 2.0 * SinT * CosT; |
---|
| 160 | CosT2 = 1.0 - 2.0 * SinT * SinT; |
---|
| 161 | endTangent = (CosT2 * vperp + SinT2 * B_x_P + vpar); |
---|
| 162 | positionMove = R * ( SinT2 * vperp + (1-CosT2) * B_x_P) + h*2 * vpar; |
---|
| 163 | |
---|
| 164 | yHelix2[0] = yIn[0] + positionMove.x(); |
---|
| 165 | yHelix2[1] = yIn[1] + positionMove.y(); |
---|
| 166 | yHelix2[2] = yIn[2] + positionMove.z(); |
---|
| 167 | yHelix2[3] = velocityVal * endTangent.x(); |
---|
| 168 | yHelix2[4] = velocityVal * endTangent.y(); |
---|
| 169 | yHelix2[5] = velocityVal * endTangent.z(); |
---|
| 170 | } |
---|
| 171 | |
---|
| 172 | // Store and/or calculate parameters for chord distance |
---|
| 173 | |
---|
| 174 | G4double ptan=velocityVal*B_v_P; |
---|
| 175 | |
---|
| 176 | G4double particleCharge = fPtrMagEqOfMot->FCof() / (eplus*c_light); |
---|
| 177 | R_Helix =std::abs( ptan/(fUnitConstant * particleCharge*Bmag)); |
---|
| 178 | |
---|
| 179 | SetAngCurve(std::abs(Theta)); |
---|
| 180 | SetCurve(std::abs(R)); |
---|
| 181 | SetRadHelix(R_Helix); |
---|
| 182 | } |
---|
| 183 | } |
---|
| 184 | |
---|
| 185 | // |
---|
| 186 | // Use the midpoint method to get an error estimate and correction |
---|
| 187 | // modified from G4ClassicalRK4: W.Wander <wwc@mit.edu> 12/09/97 |
---|
| 188 | // |
---|
| 189 | |
---|
| 190 | void |
---|
| 191 | G4MagHelicalStepper::Stepper( const G4double yInput[], |
---|
| 192 | const G4double*, |
---|
| 193 | G4double hstep, |
---|
| 194 | G4double yOut[], |
---|
| 195 | G4double yErr[] ) |
---|
| 196 | { |
---|
| 197 | const G4int nvar = 6; |
---|
| 198 | |
---|
| 199 | G4int i; |
---|
| 200 | |
---|
| 201 | // correction for Richardson Extrapolation. |
---|
| 202 | // G4double correction = 1. / ( (1 << IntegratorOrder()) -1 ); |
---|
| 203 | |
---|
| 204 | G4double yTemp[7], yIn[7] ; |
---|
| 205 | G4ThreeVector Bfld_initial, Bfld_midpoint; |
---|
| 206 | |
---|
| 207 | // Saving yInput because yInput and yOut can be aliases for same array |
---|
| 208 | |
---|
| 209 | for(i=0;i<nvar;i++) { yIn[i]=yInput[i]; } |
---|
| 210 | |
---|
| 211 | G4double h = hstep * 0.5; |
---|
| 212 | |
---|
| 213 | MagFieldEvaluate(yIn, Bfld_initial) ; |
---|
| 214 | |
---|
| 215 | // Do two half steps |
---|
| 216 | |
---|
| 217 | DumbStepper(yIn, Bfld_initial, h, yTemp); |
---|
| 218 | MagFieldEvaluate(yTemp, Bfld_midpoint) ; |
---|
| 219 | DumbStepper(yTemp, Bfld_midpoint, h, yOut); |
---|
| 220 | |
---|
| 221 | // Do a full Step |
---|
| 222 | |
---|
| 223 | h = hstep ; |
---|
| 224 | DumbStepper(yIn, Bfld_initial, h, yTemp); |
---|
| 225 | |
---|
| 226 | // Error estimation |
---|
| 227 | |
---|
| 228 | for(i=0;i<nvar;i++) |
---|
| 229 | { |
---|
| 230 | yErr[i] = yOut[i] - yTemp[i] ; |
---|
| 231 | } |
---|
| 232 | |
---|
| 233 | return; |
---|
| 234 | } |
---|
| 235 | |
---|
| 236 | G4double |
---|
| 237 | G4MagHelicalStepper::DistChord() const |
---|
| 238 | { |
---|
| 239 | // Check whether h/R > pi !! |
---|
| 240 | // Method DistLine is good only for < pi |
---|
| 241 | |
---|
| 242 | G4double Ang=GetAngCurve(); |
---|
| 243 | if(Ang<=pi) |
---|
| 244 | { |
---|
| 245 | return GetRadHelix()*(1-std::cos(0.5*Ang)); |
---|
| 246 | } |
---|
| 247 | else |
---|
| 248 | { |
---|
| 249 | if(Ang<twopi) |
---|
| 250 | { |
---|
| 251 | return GetRadHelix()*(1+std::cos(0.5*(twopi-Ang))); |
---|
| 252 | } |
---|
| 253 | else // return Diameter of projected circle |
---|
| 254 | { |
---|
| 255 | return 2*GetRadHelix(); |
---|
| 256 | } |
---|
| 257 | } |
---|
| 258 | } |
---|