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