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