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25 // 25 //
26 // G4EqEMFieldWithEDM implementation << 26 //
>> 27 // $Id: G4EqEMFieldWithEDM.cc 71664 2013-06-20 08:36:05Z gcosmo $
>> 28 //
27 // 29 //
28 // This is the standard right-hand side for e 30 // This is the standard right-hand side for equation of motion.
29 // 31 //
30 // Created: Kevin Lynch, 19.02.2009 - Based on << 32 // 19.02.2009 Kevin Lynch, based on G4EqEMFieldWithSpin
31 // Modified: Hiromi Iinuma, 06.11.2009 - see: << 33 // 06.11.2009 Hiromi Iinuma see:
32 // http://hypernews.slac.stanford.edu/HyperN << 34 // http://hypernews.slac.stanford.edu/HyperNews/geant4/get/emfields/161.html
>> 35 //
33 // ------------------------------------------- 36 // -------------------------------------------------------------------
34 37
35 #include "G4EqEMFieldWithEDM.hh" 38 #include "G4EqEMFieldWithEDM.hh"
36 #include "G4ElectroMagneticField.hh" 39 #include "G4ElectroMagneticField.hh"
37 #include "G4ThreeVector.hh" 40 #include "G4ThreeVector.hh"
38 #include "globals.hh" 41 #include "globals.hh"
39 #include "G4PhysicalConstants.hh" 42 #include "G4PhysicalConstants.hh"
40 #include "G4SystemOfUnits.hh" 43 #include "G4SystemOfUnits.hh"
41 44
42 G4EqEMFieldWithEDM::G4EqEMFieldWithEDM(G4Elect << 45 G4EqEMFieldWithEDM::G4EqEMFieldWithEDM(G4ElectroMagneticField *emField )
43 : G4EquationOfMotion( emField ) << 46 : G4EquationOfMotion( emField ), charge(0.), mass(0.), magMoment(0.),
>> 47 spin(0.), fElectroMagCof(0.), fMassCof(0.), omegac(0.),
>> 48 anomaly(0.0011659208), eta(0.), beta(0.), gamma(0.)
44 { 49 {
45 } 50 }
46 51
47 G4EqEMFieldWithEDM::~G4EqEMFieldWithEDM() = de << 52 G4EqEMFieldWithEDM::~G4EqEMFieldWithEDM()
>> 53 {
>> 54 }
48 55
49 void 56 void
50 G4EqEMFieldWithEDM::SetChargeMomentumMass(G4Ch 57 G4EqEMFieldWithEDM::SetChargeMomentumMass(G4ChargeState particleCharge,
51 G4do 58 G4double MomentumXc,
52 G4do 59 G4double particleMass)
53 { 60 {
54 charge = particleCharge.GetCharge(); << 61 charge = particleCharge.GetCharge();
55 mass = particleMass; 62 mass = particleMass;
56 magMoment = particleCharge.GetMagneticDipol 63 magMoment = particleCharge.GetMagneticDipoleMoment();
57 spin = particleCharge.GetSpin(); 64 spin = particleCharge.GetSpin();
58 65
59 fElectroMagCof = eplus*charge*c_light; 66 fElectroMagCof = eplus*charge*c_light;
60 fMassCof = mass*mass; 67 fMassCof = mass*mass;
61 68
62 omegac = (eplus/mass)*c_light; 69 omegac = (eplus/mass)*c_light;
63 70
64 G4double muB = 0.5*eplus*hbar_Planck/(mass/ 71 G4double muB = 0.5*eplus*hbar_Planck/(mass/c_squared);
65 72
66 G4double g_BMT; 73 G4double g_BMT;
67 if ( spin != 0. ) << 74 if ( spin != 0. ) g_BMT = (magMoment/muB)/spin;
68 { << 75 else g_BMT = 2.;
69 g_BMT = (std::abs(magMoment)/muB)/spin; <<
70 } <<
71 else <<
72 { <<
73 g_BMT = 2.; <<
74 } <<
75 76
76 anomaly = (g_BMT - 2.)/2.; 77 anomaly = (g_BMT - 2.)/2.;
77 78
78 G4double E = std::sqrt(sqr(MomentumXc)+sqr( 79 G4double E = std::sqrt(sqr(MomentumXc)+sqr(mass));
79 beta = MomentumXc/E; 80 beta = MomentumXc/E;
80 gamma = E/mass; 81 gamma = E/mass;
81 } 82 }
82 83
83 void 84 void
84 G4EqEMFieldWithEDM::EvaluateRhsGivenB(const G4 85 G4EqEMFieldWithEDM::EvaluateRhsGivenB(const G4double y[],
85 const G4 << 86 const G4double Field[],
86 G4 << 87 G4double dydx[] ) const
87 { 88 {
88 89
89 // Components of y: 90 // Components of y:
90 // 0-2 dr/ds, 91 // 0-2 dr/ds,
91 // 3-5 dp/ds - momentum derivatives 92 // 3-5 dp/ds - momentum derivatives
92 // 9-11 dSpin/ds = (1/beta) dSpin/dt - s 93 // 9-11 dSpin/ds = (1/beta) dSpin/dt - spin derivatives
93 94
94 // The BMT equation, following J.D.Jackson, 95 // The BMT equation, following J.D.Jackson, Classical
95 // Electrodynamics, Second Edition, with ad 96 // Electrodynamics, Second Edition, with additions for EDM
96 // evolution from 97 // evolution from
97 // M.Nowakowski, et.al. Eur.J.Phys.26, pp 5 98 // M.Nowakowski, et.al. Eur.J.Phys.26, pp 545-560, (2005)
98 // or 99 // or
99 // Silenko, Phys.Rev.ST Accel.Beams 9:03400 100 // Silenko, Phys.Rev.ST Accel.Beams 9:034003, (2006)
100 101
101 // dS/dt = (e/m) S \cross 102 // dS/dt = (e/m) S \cross
102 // MDM: [ (g/2-1 +1/\gamma) B 103 // MDM: [ (g/2-1 +1/\gamma) B
103 // -(g/2-1)\gamma/(\gamma+1) 104 // -(g/2-1)\gamma/(\gamma+1) (\beta \cdot B)\beta
104 // -(g/2-\gamma/(\gamma+1) \b 105 // -(g/2-\gamma/(\gamma+1) \beta \cross E
105 // 106 //
106 // EDM: eta/2( E - gamma/(gamma+1) \ 107 // EDM: eta/2( E - gamma/(gamma+1) \beta (\beta \cdot E)
107 // + \beta \cross B ) ] 108 // + \beta \cross B ) ]
108 // 109 //
109 // where 110 // where
110 // S = \vec{s}, where S^2 = 1 111 // S = \vec{s}, where S^2 = 1
111 // B = \vec{B} 112 // B = \vec{B}
112 // \beta = \vec{\beta} = \beta \vec{u} with 113 // \beta = \vec{\beta} = \beta \vec{u} with u^2 = 1
113 // E = \vec{E} 114 // E = \vec{E}
114 115
115 G4double pSquared = y[3]*y[3] + y[4]*y[4] + 116 G4double pSquared = y[3]*y[3] + y[4]*y[4] + y[5]*y[5] ;
116 117
117 G4double Energy = std::sqrt( pSquared + f 118 G4double Energy = std::sqrt( pSquared + fMassCof );
118 G4double cof2 = Energy/c_light ; 119 G4double cof2 = Energy/c_light ;
119 120
120 G4double pModuleInverse = 1.0/std::sqrt(pS 121 G4double pModuleInverse = 1.0/std::sqrt(pSquared) ;
121 122
122 G4double inverse_velocity = Energy * pModul 123 G4double inverse_velocity = Energy * pModuleInverse / c_light;
123 124
124 G4double cof1 = fElectroMagCof*pModuleI 125 G4double cof1 = fElectroMagCof*pModuleInverse ;
125 126
126 dydx[0] = y[3]*pModuleInverse ; 127 dydx[0] = y[3]*pModuleInverse ;
127 dydx[1] = y[4]*pModuleInverse ; 128 dydx[1] = y[4]*pModuleInverse ;
128 dydx[2] = y[5]*pModuleInverse ; 129 dydx[2] = y[5]*pModuleInverse ;
129 130
130 dydx[3] = cof1*(cof2*Field[3] + (y[4]*Field 131 dydx[3] = cof1*(cof2*Field[3] + (y[4]*Field[2] - y[5]*Field[1])) ;
131 132
132 dydx[4] = cof1*(cof2*Field[4] + (y[5]*Field 133 dydx[4] = cof1*(cof2*Field[4] + (y[5]*Field[0] - y[3]*Field[2])) ;
133 134
134 dydx[5] = cof1*(cof2*Field[5] + (y[3]*Field 135 dydx[5] = cof1*(cof2*Field[5] + (y[3]*Field[1] - y[4]*Field[0])) ;
135 136
136 dydx[6] = dydx[8] = 0.;//not used 137 dydx[6] = dydx[8] = 0.;//not used
137 138
138 // Lab Time of flight 139 // Lab Time of flight
139 dydx[7] = inverse_velocity; 140 dydx[7] = inverse_velocity;
140 141
141 G4ThreeVector BField(Field[0],Field[1],Fiel 142 G4ThreeVector BField(Field[0],Field[1],Field[2]);
142 G4ThreeVector EField(Field[3],Field[4],Fiel 143 G4ThreeVector EField(Field[3],Field[4],Field[5]);
143 144
144 EField /= c_light; 145 EField /= c_light;
145 146
146 G4ThreeVector u(y[3], y[4], y[5]); 147 G4ThreeVector u(y[3], y[4], y[5]);
147 u *= pModuleInverse; 148 u *= pModuleInverse;
148 149
149 G4double udb = anomaly*beta*gamma/(1.+gamma 150 G4double udb = anomaly*beta*gamma/(1.+gamma) * (BField * u);
150 G4double ucb = (anomaly+1./gamma)/beta; 151 G4double ucb = (anomaly+1./gamma)/beta;
151 G4double uce = anomaly + 1./(gamma+1.); 152 G4double uce = anomaly + 1./(gamma+1.);
152 G4double ude = beta*gamma/(1.+gamma)*(EFiel 153 G4double ude = beta*gamma/(1.+gamma)*(EField*u);
153 154
154 G4ThreeVector Spin(y[9],y[10],y[11]); 155 G4ThreeVector Spin(y[9],y[10],y[11]);
155 156
156 G4double pcharge; 157 G4double pcharge;
157 if (charge == 0.) << 158 if (charge == 0.) pcharge = 1.;
158 { << 159 else pcharge = charge;
159 pcharge = 1.; <<
160 } <<
161 else <<
162 { <<
163 pcharge = charge; <<
164 } <<
165 160
166 G4ThreeVector dSpin(0.,0.,0.); 161 G4ThreeVector dSpin(0.,0.,0.);
167 if (Spin.mag2() != 0.) << 162 if (Spin.mag2() != 0.) {
168 { << 163 dSpin =
169 dSpin = pcharge*omegac*( ucb*(Spin.cross << 164 pcharge*omegac*( ucb*(Spin.cross(BField))-udb*(Spin.cross(u))
170 // from Jacks 165 // from Jackson
171 // -uce*Spin. 166 // -uce*Spin.cross(u.cross(EField)) )
172 // but this f 167 // but this form has one less operation
173 - uce*(u*(Spin*EField 168 - uce*(u*(Spin*EField) - EField*(Spin*u))
174 + eta/2.*(Spin.cross( 169 + eta/2.*(Spin.cross(EField) - ude*(Spin.cross(u))
175 // +Spin.cros 170 // +Spin.cross(u.cross(Bfield))
176 + (u*(Spin*BField) - 171 + (u*(Spin*BField) - BField*(Spin*u)) ) );
177 } 172 }
178 173
179 dydx[ 9] = dSpin.x(); 174 dydx[ 9] = dSpin.x();
180 dydx[10] = dSpin.y(); 175 dydx[10] = dSpin.y();
181 dydx[11] = dSpin.z(); 176 dydx[11] = dSpin.z();
182 177
183 return; << 178 return ;
184 } 179 }
185 180