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24 // ******************************************* 24 // ********************************************************************
25 // 25 //
26 // G4RepleteEofM implementation 26 // G4RepleteEofM implementation
27 // 27 //
28 // Created: P.Gumplinger, 08.04.2013 28 // Created: P.Gumplinger, 08.04.2013
29 // ------------------------------------------- 29 // -------------------------------------------------------------------
30 30
31 #include "G4RepleteEofM.hh" 31 #include "G4RepleteEofM.hh"
32 #include "G4Field.hh" 32 #include "G4Field.hh"
33 #include "G4ThreeVector.hh" 33 #include "G4ThreeVector.hh"
34 #include "globals.hh" 34 #include "globals.hh"
35 35
36 #include "G4PhysicalConstants.hh" 36 #include "G4PhysicalConstants.hh"
37 #include "G4SystemOfUnits.hh" 37 #include "G4SystemOfUnits.hh"
38 38
39 39
40 G4RepleteEofM::G4RepleteEofM( G4Field* field, 40 G4RepleteEofM::G4RepleteEofM( G4Field* field, G4int nvar )
41 : G4EquationOfMotion( field ), fNvar 41 : G4EquationOfMotion( field ), fNvar(nvar)
42 { 42 {
43 fGfield = field->IsGravityActive(); 43 fGfield = field->IsGravityActive();
44 } 44 }
45 45
46 G4RepleteEofM::~G4RepleteEofM() = default; 46 G4RepleteEofM::~G4RepleteEofM() = default;
47 47
48 void 48 void
49 G4RepleteEofM::SetChargeMomentumMass(G4ChargeS 49 G4RepleteEofM::SetChargeMomentumMass(G4ChargeState particleCharge, // e+ units
50 G4double Momentu 50 G4double MomentumXc,
51 G4double particl 51 G4double particleMass)
52 { 52 {
53 charge = particleCharge.GetCharge(); 53 charge = particleCharge.GetCharge();
54 mass = particleMass; 54 mass = particleMass;
55 magMoment = particleCharge.GetMagneticDipol 55 magMoment = particleCharge.GetMagneticDipoleMoment();
56 spin = particleCharge.GetSpin(); 56 spin = particleCharge.GetSpin();
57 57
58 ElectroMagCof = eplus*charge*c_light; 58 ElectroMagCof = eplus*charge*c_light;
59 omegac = (eplus/mass)*c_light; 59 omegac = (eplus/mass)*c_light;
60 60
61 G4double muB = 0.5*eplus*hbar_Planck/(mass/ 61 G4double muB = 0.5*eplus*hbar_Planck/(mass/c_squared);
62 62
63 G4double g_BMT; 63 G4double g_BMT;
64 if ( spin != 0. ) 64 if ( spin != 0. )
65 { 65 {
66 g_BMT = (std::abs(magMoment)/muB)/spin; 66 g_BMT = (std::abs(magMoment)/muB)/spin;
67 } 67 }
68 else 68 else
69 { 69 {
70 g_BMT = 2.; 70 g_BMT = 2.;
71 } 71 }
72 72
73 anomaly = (g_BMT - 2.)/2.; 73 anomaly = (g_BMT - 2.)/2.;
74 74
75 G4double E = std::sqrt(sqr(MomentumXc)+sqr( 75 G4double E = std::sqrt(sqr(MomentumXc)+sqr(mass));
76 beta = MomentumXc/E; 76 beta = MomentumXc/E;
77 gamma = E/mass; 77 gamma = E/mass;
78 } 78 }
79 79
80 void 80 void
81 G4RepleteEofM::EvaluateRhsGivenB( const G4doub 81 G4RepleteEofM::EvaluateRhsGivenB( const G4double y[],
82 const G4doub 82 const G4double Field[],
83 G4doub 83 G4double dydx[] ) const
84 { 84 {
85 85
86 // Components of y: 86 // Components of y:
87 // 0-2 dr/ds, 87 // 0-2 dr/ds,
88 // 3-5 dp/ds - momentum derivatives 88 // 3-5 dp/ds - momentum derivatives
89 // 9-11 dSpin/ds = (1/beta) dSpin/dt - s 89 // 9-11 dSpin/ds = (1/beta) dSpin/dt - spin derivatives
90 // 90 //
91 // The BMT equation, following J.D.Jackson, 91 // The BMT equation, following J.D.Jackson, Classical
92 // Electrodynamics, Second Edition, 92 // Electrodynamics, Second Edition,
93 // dS/dt = (e/mc) S \cross 93 // dS/dt = (e/mc) S \cross
94 // [ (g/2-1 +1/\gamma) B 94 // [ (g/2-1 +1/\gamma) B
95 // -(g/2-1)\gamma/(\gamma+1) 95 // -(g/2-1)\gamma/(\gamma+1) (\beta \cdot B)\beta
96 // -(g/2-\gamma/(\gamma+1) \b 96 // -(g/2-\gamma/(\gamma+1) \beta \cross E ]
97 // where 97 // where
98 // S = \vec{s}, where S^2 = 1 98 // S = \vec{s}, where S^2 = 1
99 // B = \vec{B} 99 // B = \vec{B}
100 // \beta = \vec{\beta} = \beta \vec{u} with 100 // \beta = \vec{\beta} = \beta \vec{u} with u^2 = 1
101 // E = \vec{E} 101 // E = \vec{E}
102 // 102 //
103 // Field[0,1,2] are the magnetic field comp 103 // Field[0,1,2] are the magnetic field components
104 // Field[3,4,5] are the electric field comp 104 // Field[3,4,5] are the electric field components
105 // Field[6,7,8] are the gravity field comp 105 // Field[6,7,8] are the gravity field components
106 // The Field[] array may trivially be exten 106 // The Field[] array may trivially be extended to 18 components
107 // Field[ 9] == dB_x/dx; Field[10] == dB_y/ 107 // Field[ 9] == dB_x/dx; Field[10] == dB_y/dx; Field[11] == dB_z/dx
108 // Field[12] == dB_x/dy; Field[13] == dB_y/ 108 // Field[12] == dB_x/dy; Field[13] == dB_y/dy; Field[14] == dB_z/dy
109 // Field[15] == dB_x/dz; Field[16] == dB_y/ 109 // Field[15] == dB_x/dz; Field[16] == dB_y/dz; Field[17] == dB_z/dz
110 110
111 G4double momentum_mag_square = y[3]*y[3] + 111 G4double momentum_mag_square = y[3]*y[3] + y[4]*y[4] + y[5]*y[5];
112 G4double inv_momentum_magnitude = 1.0 / std 112 G4double inv_momentum_magnitude = 1.0 / std::sqrt( momentum_mag_square );
113 113
114 G4double Energy = std::sqrt(momentum_mag_sq 114 G4double Energy = std::sqrt(momentum_mag_square + mass*mass);
115 G4double inverse_velocity = Energy*inv_mome 115 G4double inverse_velocity = Energy*inv_momentum_magnitude/c_light;
116 116
117 G4double cof1 = ElectroMagCof*inv_momentum_ 117 G4double cof1 = ElectroMagCof*inv_momentum_magnitude;
118 G4double cof2 = Energy/c_light; 118 G4double cof2 = Energy/c_light;
119 G4double cof3 = inv_momentum_magnitude*mass 119 G4double cof3 = inv_momentum_magnitude*mass;
120 120
121 dydx[0] = y[3]*inv_momentum_magnitude; 121 dydx[0] = y[3]*inv_momentum_magnitude; // (d/ds)x = Vx/V
122 dydx[1] = y[4]*inv_momentum_magnitude; 122 dydx[1] = y[4]*inv_momentum_magnitude; // (d/ds)y = Vy/V
123 dydx[2] = y[5]*inv_momentum_magnitude; 123 dydx[2] = y[5]*inv_momentum_magnitude; // (d/ds)z = Vz/V
124 124
125 dydx[3] = 0.; 125 dydx[3] = 0.;
126 dydx[4] = 0.; 126 dydx[4] = 0.;
127 dydx[5] = 0.; 127 dydx[5] = 0.;
128 128
129 G4double field[18] = {0.,0.,0.,0.,0.,0.,0., 129 G4double field[18] = {0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.,0.};
130 130
131 field[0] = Field[0]; 131 field[0] = Field[0];
132 field[1] = Field[1]; 132 field[1] = Field[1];
133 field[2] = Field[2]; 133 field[2] = Field[2];
134 134
135 // Force due to B field - Field[0,1,2] 135 // Force due to B field - Field[0,1,2]
136 136
137 if (fBfield) 137 if (fBfield)
138 { 138 {
139 if (charge != 0.) 139 if (charge != 0.)
140 { 140 {
141 dydx[3] += cof1*(y[4]*field[2] - y[5] 141 dydx[3] += cof1*(y[4]*field[2] - y[5]*field[1]);
142 dydx[4] += cof1*(y[5]*field[0] - y[3] 142 dydx[4] += cof1*(y[5]*field[0] - y[3]*field[2]);
143 dydx[5] += cof1*(y[3]*field[1] - y[4] 143 dydx[5] += cof1*(y[3]*field[1] - y[4]*field[0]);
144 } 144 }
145 } 145 }
146 146
147 // add force due to E field - Field[3,4,5] 147 // add force due to E field - Field[3,4,5]
148 148
149 if (!fBfield) 149 if (!fBfield)
150 { 150 {
151 field[3] = Field[0]; 151 field[3] = Field[0];
152 field[4] = Field[1]; 152 field[4] = Field[1];
153 field[5] = Field[2]; 153 field[5] = Field[2];
154 } 154 }
155 else 155 else
156 { 156 {
157 field[3] = Field[3]; 157 field[3] = Field[3];
158 field[4] = Field[4]; 158 field[4] = Field[4];
159 field[5] = Field[5]; 159 field[5] = Field[5];
160 } 160 }
161 161
162 if (fEfield) 162 if (fEfield)
163 { 163 {
164 if (charge != 0.) 164 if (charge != 0.)
165 { 165 {
166 dydx[3] += cof1*cof2*field[3]; 166 dydx[3] += cof1*cof2*field[3];
167 dydx[4] += cof1*cof2*field[4]; 167 dydx[4] += cof1*cof2*field[4];
168 dydx[5] += cof1*cof2*field[5]; 168 dydx[5] += cof1*cof2*field[5];
169 } 169 }
170 } 170 }
171 171
172 // add force due to gravity field - Field[6 172 // add force due to gravity field - Field[6,7,8]
173 173
174 if (!fBfield && !fEfield) 174 if (!fBfield && !fEfield)
175 { 175 {
176 field[6] = Field[0]; 176 field[6] = Field[0];
177 field[7] = Field[1]; 177 field[7] = Field[1];
178 field[8] = Field[2]; 178 field[8] = Field[2];
179 } 179 }
180 else 180 else
181 { 181 {
182 field[6] = Field[6]; 182 field[6] = Field[6];
183 field[7] = Field[7]; 183 field[7] = Field[7];
184 field[8] = Field[8]; 184 field[8] = Field[8];
185 } 185 }
186 186
187 if (fGfield) 187 if (fGfield)
188 { 188 {
189 if (mass > 0.) 189 if (mass > 0.)
190 { 190 {
191 dydx[3] += field[6]*cof2*cof3/c_light 191 dydx[3] += field[6]*cof2*cof3/c_light;
192 dydx[4] += field[7]*cof2*cof3/c_light 192 dydx[4] += field[7]*cof2*cof3/c_light;
193 dydx[5] += field[8]*cof2*cof3/c_light 193 dydx[5] += field[8]*cof2*cof3/c_light;
194 } 194 }
195 } 195 }
196 196
197 // add force 197 // add force
198 198
199 if (!fBfield && !fEfield && !fGfield) 199 if (!fBfield && !fEfield && !fGfield)
200 { 200 {
201 field[9] = Field[0]; 201 field[9] = Field[0];
202 field[10] = Field[1]; 202 field[10] = Field[1];
203 field[11] = Field[2]; 203 field[11] = Field[2];
204 field[12] = Field[3]; 204 field[12] = Field[3];
205 field[13] = Field[4]; 205 field[13] = Field[4];
206 field[14] = Field[5]; 206 field[14] = Field[5];
207 field[15] = Field[6]; 207 field[15] = Field[6];
208 field[16] = Field[7]; 208 field[16] = Field[7];
209 field[17] = Field[8]; 209 field[17] = Field[8];
210 } 210 }
211 else 211 else
212 { 212 {
213 field[9] = Field[9]; 213 field[9] = Field[9];
214 field[10] = Field[10]; 214 field[10] = Field[10];
215 field[11] = Field[11]; 215 field[11] = Field[11];
216 field[12] = Field[12]; 216 field[12] = Field[12];
217 field[13] = Field[13]; 217 field[13] = Field[13];
218 field[14] = Field[14]; 218 field[14] = Field[14];
219 field[15] = Field[15]; 219 field[15] = Field[15];
220 field[16] = Field[16]; 220 field[16] = Field[16];
221 field[17] = Field[17]; 221 field[17] = Field[17];
222 } 222 }
223 223
224 if (fgradB) 224 if (fgradB)
225 { 225 {
226 if (magMoment != 0.) 226 if (magMoment != 0.)
227 { 227 {
228 dydx[3] += magMoment*(y[9]*field[ 9]+ 228 dydx[3] += magMoment*(y[9]*field[ 9]+y[10]*field[10]+y[11]*field[11])
229 229 *inv_momentum_magnitude*Energy;
230 dydx[4] += magMoment*(y[9]*field[12]+ 230 dydx[4] += magMoment*(y[9]*field[12]+y[10]*field[13]+y[11]*field[14])
231 231 *inv_momentum_magnitude*Energy;
232 dydx[5] += magMoment*(y[9]*field[15]+ 232 dydx[5] += magMoment*(y[9]*field[15]+y[10]*field[16]+y[11]*field[17])
233 233 *inv_momentum_magnitude*Energy;
234 } 234 }
235 } 235 }
236 236
237 dydx[6] = 0.; // not used 237 dydx[6] = 0.; // not used
238 238
239 // Lab Time of flight 239 // Lab Time of flight
240 // 240 //
241 dydx[7] = inverse_velocity; 241 dydx[7] = inverse_velocity;
242 242
243 if (fNvar == 12) 243 if (fNvar == 12)
244 { 244 {
245 dydx[ 8] = 0.; //not used 245 dydx[ 8] = 0.; //not used
246 246
247 dydx[ 9] = 0.; 247 dydx[ 9] = 0.;
248 dydx[10] = 0.; 248 dydx[10] = 0.;
249 dydx[11] = 0.; 249 dydx[11] = 0.;
250 } 250 }
251 251
252 if (fSpin) 252 if (fSpin)
253 { 253 {
254 G4ThreeVector BField(0.,0.,0.); 254 G4ThreeVector BField(0.,0.,0.);
255 if (fBfield) 255 if (fBfield)
256 { 256 {
257 G4ThreeVector F(field[0],field[1],fie 257 G4ThreeVector F(field[0],field[1],field[2]);
258 BField = F; 258 BField = F;
259 } 259 }
260 260
261 G4ThreeVector EField(0.,0.,0.); 261 G4ThreeVector EField(0.,0.,0.);
262 if (fEfield) 262 if (fEfield)
263 { 263 {
264 G4ThreeVector F(field[3],field[4],fie 264 G4ThreeVector F(field[3],field[4],field[5]);
265 EField = F; 265 EField = F;
266 } 266 }
267 267
268 EField /= c_light; 268 EField /= c_light;
269 269
270 G4ThreeVector u(y[3], y[4], y[5]); 270 G4ThreeVector u(y[3], y[4], y[5]);
271 u *= inv_momentum_magnitude; 271 u *= inv_momentum_magnitude;
272 272
273 G4double udb = anomaly*beta*gamma/(1.+ga 273 G4double udb = anomaly*beta*gamma/(1.+gamma) * (BField * u);
274 G4double ucb = (anomaly+1./gamma)/beta; 274 G4double ucb = (anomaly+1./gamma)/beta;
275 G4double uce = anomaly + 1./(gamma+1.); 275 G4double uce = anomaly + 1./(gamma+1.);
276 276
277 G4ThreeVector Spin(y[9],y[10],y[11]); 277 G4ThreeVector Spin(y[9],y[10],y[11]);
278 278
279 G4double pcharge; 279 G4double pcharge;
280 if (charge == 0.) 280 if (charge == 0.)
281 { 281 {
282 pcharge = 1.; 282 pcharge = 1.;
283 } 283 }
284 else 284 else
285 { 285 {
286 pcharge = charge; 286 pcharge = charge;
287 } 287 }
288 288
289 G4ThreeVector dSpin(0.,0.,0); 289 G4ThreeVector dSpin(0.,0.,0);
290 if (Spin.mag2() != 0.) 290 if (Spin.mag2() != 0.)
291 { 291 {
292 if (fBfield) 292 if (fBfield)
293 { 293 {
294 dSpin = 294 dSpin =
295 pcharge*omegac*( ucb*(Spin.cross( 295 pcharge*omegac*( ucb*(Spin.cross(BField))-udb*(Spin.cross(u)) );
296 } 296 }
297 if (fEfield) 297 if (fEfield)
298 { 298 {
299 dSpin -= pcharge*omegac*( uce*(u*( 299 dSpin -= pcharge*omegac*( uce*(u*(Spin*EField) - EField*(Spin*u)) );
300 // from Jackson 300 // from Jackson
301 // -uce*Spin.cross(u.cross(EFiel 301 // -uce*Spin.cross(u.cross(EField)) );
302 // but this form has one less op 302 // but this form has one less operation
303 } 303 }
304 } 304 }
305 305
306 dydx[ 9] = dSpin.x(); 306 dydx[ 9] = dSpin.x();
307 dydx[10] = dSpin.y(); 307 dydx[10] = dSpin.y();
308 dydx[11] = dSpin.z(); 308 dydx[11] = dSpin.z();
309 } 309 }
310 310
311 return; 311 return;
312 } 312 }
313 313