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