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