{
"metadata": {
"name": "",
"signature": "sha256:9b22acc9bcbd27c33c9e62b557ecc66fc981e9c1775b58e8ee670ca880259cf2"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter11-Particle Accelerators"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex1-pg535"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.1 : : Page-535(2011) \n",
"#calculate The optimum number of stages in the accelerator and the ripple voltage\n",
"import math\n",
"V_0 = 10**5; ## Accelerating voltage, volts\n",
"C = 0.02e-006; ## Capacitance, farad\n",
"I = 4*1e-003; ## Current, ampere\n",
"f = 200.; ## Frequency, cycles per sec\n",
"n = math.sqrt (V_0*f*C/I); ## Number of particles\n",
"delta_V = I*n*(n+1.)/(4.*f*C);\n",
"print'%s %.2f %s'%(\"\\nThe optimum number of stages in the accelerator = \", n,\"\");\n",
"print'%s %.2f %s'%(\"\\nThe ripple voltage = \", delta_V/1e+003,\"kV\");\n",
"\n",
"## Result\n",
"## The optimum number of stages in the accelerator = 10\n",
"## The ripple voltage = 27.5 kV \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The optimum number of stages in the accelerator = 10.00 \n",
"\n",
"The ripple voltage = 27.50 kV\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg536"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.2 : : Page-536 (2011)\n",
"#calculate The charging current and The rate of rise of electrode potential\n",
"import math\n",
"s = 15.; ## Speed, metre per sec\n",
"w = 0.3; ## Width of the electrode, metre\n",
"E = 3e+06; ## Breakdown strength, volts per metre\n",
"eps = 8.85e-12; ## Absolute permitivity of free space, farad per metre\n",
"C = 111e-12; ## Capacitance, farad\n",
"i = round (2*eps*E*s*w*10**6); ## Current, micro ampere\n",
"V = i/C*10**-12; ## Rate of rise of electrode potential, mega volts per sec\n",
"print'%s %.2f %s %.2f %s '%(\"\\nThe charging current =\",i,\" micro-ampere\"and \" \\nThe rate of rise of electrode potential = \",V,\" MV/sec\");\n",
"\n",
"## Result\n",
"## The charging current = 239 micro-ampere \n",
"## The rate of rise of electrode potential = 2.15 MV/sec "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The charging current = 239.00 \n",
"The rate of rise of electrode potential = 2.15 MV/sec \n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg536"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.3 : : Page-536 (2011)\n",
"#calculate The length of the final drift tube and The kinetic energy of the injected protons\n",
"import math\n",
"import scipy\n",
"from scipy import integrate\n",
"\n",
"f = 200.*10**6; ## Frequency of the accelerator, cycle per sec\n",
"M = 1.6724e-27; ## Mass of the proton, Kg\n",
"E = 45.3*1.6e-13; ## Accelerating energy, joule\n",
"L_f = round (1./f*math.sqrt(2.*E/M)*100.); ## Length of the final drift tube, centi metre\n",
"L_1 = 5.35*10**-2; ## Length of the first drift tube, metre\n",
"K_E = (1./2.*M*L_1**2.*f**2.)/1.6e-13; ## Kinetic energy of the injected proton, MeV\n",
"E_inc = E/1.6e-13-K_E; ## Increase in energy, MeV\n",
"q = 1.6e-19; ## Charge of the proton, C\n",
"V = 1.49e+06; ## Accelerating voltage, volts\n",
"N = E_inc*1.6e-13/(q*V); ## Number of drift protons\n",
"def fun(n):\n",
" y=n**0.5\n",
" return y\n",
"\n",
"l2=scipy.integrate.quad(fun,0,N)\n",
"L = 1./f*math.sqrt(2.*q*V/M)*l2[0]; ## Total length of the accelerator, metre\n",
"print'%s %.2f %s %.2f %s %.2f %s '%(\"\\nThe length of the final drift tube = \",L_f,\" cm\"and\"\\nThe kinetic energy of the injected protons = \",K_E,\" MeV\"and\"\\nThe total length of the accelerator = \",L,\" metre\");\n",
"\n",
"## Result\n",
"## The length of the final drift tube = 47 cm\n",
"## The kinetic energy of the injected protons = 0.60 MeV\n",
"## The total length of the accelerator = 9.2 metre "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The length of the final drift tube = 47.00 \n",
"The kinetic energy of the injected protons = 0.60 \n",
"The total length of the accelerator = 9.25 metre \n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg536"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.5 : : Page-536 (2011)\n",
"#find energy of the emergine deutron and frequency of the dee voltage\n",
"import math\n",
"B = 1.4; ## Magnetic field, tesla\n",
"R = 88e-002; ## Radius of the orbit, metre\n",
"q = 1.6023e-019; ## Charge of the deutron, C\n",
"M_d = 2.014102*1.66e-27; ## Mass of the deutron, Kg\n",
"M_He = 4.002603*1.66e-27; ## Mass of the He ion, Kg\n",
"E = B**2*R**2*q**2/(2*M_d*1.6e-13); ## Energy og the emerging deutron, mega electron volts\n",
"f = B*q/(2.*math.pi*M_d)*10**-6; ## Frequency of the deutron voltage, mega cycles per sec\n",
"B_He = 2*math.pi*M_He*f*10**6/(2*q); ## Magnetic field required for He(++) ions, weber per square metre\n",
"B_change = B-B_He; ## Change in magnetic field, tesla\n",
"print'%s %.2f %s %.2f %s %.2f %s '%(\"\\nThe energy of the emerging deutron = \",E,\" MeV\" and \"\\nThe frequency of the dee voltage = \",f,\"MHz\" and\"\\nThe change in magnetic field = \",B_change,\" tesla\");\n",
"\n",
"## Result\n",
"## The energy of the emerging deutron = 36.4 MeV\n",
"## The frequency of the dee voltage = 10.68 MHz\n",
"## The change in magnetic field = 0.01 tesla "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The energy of the emerging deutron = 36.42 \n",
"The frequency of the dee voltage = 10.68 \n",
"The change in magnetic field = 0.01 tesla \n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg537"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.6: : Page-537 (2011)\n",
"#calculate effective reduction in magnetic field and charge in orbit radius\n",
"import math\n",
"K_E = 7.5*1.6023e-13; ## Kinetic energy, joule \n",
"r = 0.51; ## Radius of the proton's orbit, metre\n",
"E = 5*10**6; ## Electric field, volts per metre\n",
"m = 1.67e-27; ## Mass of the proton, Kg\n",
"q = 1.6023e-19; ## Charge of the proton, C\n",
"v = math.sqrt(2.*K_E/m); ## Velocity of the proton, metre per sec\n",
"B_red = E/v; ## The effective reduction in magnetic field, tesla\n",
"B = m*v/(q*r); ## Total magnetic field produced, tesla\n",
"r_change = r*B_red/B; ## The change in orbit radius, metre\n",
"print'%s %.2f %s %.2f %s '%(\"\\nThe effective reduction in magnetic field = \",B_red,\" tesla \"and \"\\nThe change in orbit radius = \",r_change,\" metre \");\n",
"\n",
"## Result\n",
"## The effective reduction in magnetic field = 0.132 tesla \n",
"## The change in orbit radius = 0.087 metre "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The effective reduction in magnetic field = 0.13 \n",
"The change in orbit radius = 0.09 metre \n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg537"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.7 : : Page-537 (2011)\n",
"#calculate enegy of the elctron and average enegy gained per revolution \n",
"import math\n",
"B = 0.4; ## Magnetic field, tesla\n",
"e = 1.6203e-19; ## Charge of an electron, C\n",
"R = 30*2.54e-02; ## Radius, metre\n",
"c = 3e+08; ## Capacitance, farad\n",
"E = B*e*R*c/1.6e-13; ## The energy of the electron, mega electron volts\n",
"f = 50.; ## Frequency, cycles per sec\n",
"N = c/(4*2*math.pi*f*R); ## Total number of revolutions\n",
"Avg_E_per_rev = E*1e+006/N; ## Average energy gained per revolution, electron volt\n",
"print'%s %.2f %s %.2f %s '%(\"\\nThe energy of the electron = \",E,\" MeV\"and \"\\nThe average energy gained per revolution = \",Avg_E_per_rev,\" eV\");\n",
"\n",
"## Result\n",
"## The energy of the electron = 92.6 MeV\n",
"## The average energy gained per revolution = 295.57 eV \n",
"## Note: Wrong answer is given in the textbook \n",
"## Average energy gained per revolution : 295.57 electron volts\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The energy of the electron = 92.60 \n",
"The average energy gained per revolution = 295.57 eV \n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8-pg537"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.8 : : Page-537 (2011)\n",
"#calculate peak current and average current and duty cycle\n",
"import math\n",
"R = 0.35; ## Orbit radius, metre\n",
"N = 100e+06/480.; ## Total number of revolutions\n",
"L = 2*math.pi*R*N; ## Distance traversed by the electron, metre\n",
"t = 2e-06; ## Pulse duration, sec\n",
"e = 1.6203e-19; ## Charge of an electron, C\n",
"n = 3e+09; ## Number of electrons\n",
"f = 180.; ## frequency, hertz\n",
"I_p = n*e/t; ## Peak current, ampere\n",
"I_avg = n*e*f; ## Average current, ampere \n",
"tau = t*f; ## Duty cycle\n",
"print'%s %.2e %s %.2e %s %.2e %s'%(\"\\nThe peak current = \",I_p,\" ampere\" and \"\\nThe average current = \",I_avg,\" ampere \"and \"\\nThe duty cycle =\",tau,\"\");\n",
"\n",
"## Result\n",
"## The peak current = 2.4e-004 ampere \n",
"## The average current = 8.75e-008 ampere \n",
"## The duty cycle = 3.6e-004 \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The peak current = 2.43e-04 \n",
"The average current = 8.75e-08 \n",
"The duty cycle = 3.60e-04 \n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9-pg538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.9 : : Page-538 (2011)\n",
"#calculate maximum frequncy of the dee voltage and kinetic energy of the deutron \n",
"import math\n",
"q = 1.6023e-19; ## Charge of an electron, C\n",
"B_0 = 1.5; ## Magnetic field at the centre, tesla\n",
"m_d = 2.014102*1.66e-27; ## Mass of the deutron, Kg\n",
"f_max = B_0*q/(2*math.pi*m_d*10**6); ## Maximum frequency of the dee voltage, mega cycles per sec\n",
"B_prime = 1.4310; ## Magnetic field at the periphery of the dee, tesla\n",
"f_prime = 10**7; ## Frequency, cycles per sec\n",
"c = 3e+08; ## Velocity of the light, metre per sec\n",
"M = B_prime*q/(2*math.pi*f_prime*1.66e-27); ## Relativistic mass, u\n",
"K_E = (M-m_d/1.66e-27)*931.5; ## Kinetic energy of the particle, mega electron volts\n",
"print'%s %.2f %s %.2f %s '%(\"\\nThe maximum frequency of the dee voltage = \",f_max,\" MHz\"and \"\\nThe kinetic energy of the deuteron = \",K_E,\" MeV\");\n",
" \n",
"## Result\n",
"## The maximum frequency of the dee voltage = 11.44 MHz\n",
"## The kinetic energy of the deuteron = 171.6 MeV \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The maximum frequency of the dee voltage = 11.44 \n",
"The kinetic energy of the deuteron = 171.62 MeV \n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10-pg538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate frequency of the applied electric field and magnetic field intensity\n",
"## Exa11.10 : : Page-538 (2011)\n",
"import math\n",
"e = 1.6023e-19; ## Charge of an electron, C\n",
"E = 70*1.6e-13; ## Energy, electron volts\n",
"R = 0.28; ## Radius of the orbit, metre\n",
"c = 3e+08; ## Velocity of light, metre per sec\n",
"B = E/(e*R*c); ## Magnetic field intensity, tesla\n",
"f = e*B*c**2/(2*math.pi*E); ## Frequency, cycle per sec\n",
"del_E = 88.5*(0.07)**4*10**3/(R); ## Energy radiated by an electron, electron volts\n",
"print'%s %.2f %s %.2f %s %.2f %s '%(\"\\nThe frequency of the applied electric field = \",f,\" cycles per sec\" and\"\\nThe magnetic field intensity = \",B,\" tesla\"and \"\\nThe energy radiated by the electron =\",del_E,\" eV\");\n",
"\n",
"## Result\n",
"## The frequency of the applied electric field = 1.705e+008 cycles per sec \n",
"## The magnetic field intensity = 0.832 tesla\n",
"## The energy radiated by the electron = 7.6 eV "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The frequency of the applied electric field = 170523153.31 \n",
"The magnetic field intensity = 0.83 \n",
"The energy radiated by the electron = 7.59 eV \n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex11-pg538"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate kinetic energy of the accelerated nitrogen\n",
"## Exa11.11 : : Page-538 (2011)\n",
"import math\n",
"E = 3.; ## Energy of proton synchrotron, giga electron volts\n",
"m_0_c_sq = 0.938; ## Relativistic energy, mega electron volts\n",
"P_p = math.sqrt(E**2-m_0_c_sq**2); ## Momentum of the proton, giga electron volts per c\n",
"P_n = 6*P_p; ## Momentum of the N(14) ions, giga electron volts\n",
"T_n = math.sqrt(P_n**2+(0.938*14.)**2)-0.938*14; ## Kinetic energy of the accelerated nitrogen ion\n",
"print'%s %.2f %s'%(\"\\nThe kinetic energy of the accelerated nitrogen ion = \",T_n,\" MeV\");\n",
"\n",
"## Result\n",
"## The kinetic energy of the accelerated nitrogen ion = 8.43 MeV \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The kinetic energy of the accelerated nitrogen ion = 8.43 MeV\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex12-pg539"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Exa11.12 : : Page-539 (2011)\n",
"#calculate maximum magnetic flux density and maximum frequency of the accerlating voltage\n",
"import math\n",
"e = 1.6e-19; ## Charge of an electron, C\n",
"R = 9.144; ## Radius, metre\n",
"m_p = 1.67e-027; ## Mass of the proton, Kg\n",
"E = 3.6*1.6e-13; ## Energy, joule\n",
"L = 3.048; ## Length of the one synchrotron section, metre \n",
"T = 3; ## Kinetic energy, giga electron volts\n",
"c = 3e+08; ## Velocity of the light, metre per sec\n",
"m_0_c_sq = 0.938; ## Relativistic energy, mega electron volts\n",
"B = round (math.sqrt(2*m_p*E)/(R*e)*10**4); ## Maximum magnetic field density, web per square metre\n",
"v = B*10**-4*e*R/m_p; ## Velocity of the proton, metre per sec\n",
"f_c = v/(2*math.pi*R*10**6); ## Frequency of the circular orbit, mega cycles per sec\n",
"f_0 = 2*math.pi*R*f_c*10**3/(2*math.pi*R+4*L); ## Reduced frequency, kilo cycles per sec\n",
"B_m = 3.33*math.sqrt(T*(T+2*m_0_c_sq))/R; ## Relativistic field, web per square metre\n",
"f_0 = c**2*e*R*B*1e-004/((2*math.pi*R+4*L)*(T+m_0_c_sq)*e*1e+015); ## Maximum frequency of the accelerating voltage, mega cycles per sec\n",
"print'%s %.2f %s %.2f %s '%(\"\\nThe maximum magnetic flux density = \",B_m,\" weber/Sq.m\"and \"\\nThe maximum frequency of the accelerating voltage = \",f_0,\" MHz\");\n",
" \n",
"## Result\n",
"## The maximum magnetic flux density = 1.393 weber/Sq.m\n",
"## The maximum frequency of the accelerating voltage = 0.09 MHz\n",
"## Answer is given wrongly in the textbook \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The maximum magnetic flux density = 1.39 \n",
"The maximum frequency of the accelerating voltage = 0.09 MHz \n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex13-pg539"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate energy of the proton\n",
"## Exa11.13 : : Page-539 (2011)\n",
"import math\n",
"E_c = 30e+009; ## Energy of the proton accelerator, GeV\n",
"m_0_c_sq = 0.938*10**6; ## Relativistic energy, GeV\n",
"E_p = (4*E_c**2-2*m_0_c_sq**2)/(2*m_0_c_sq) ; ## Energy of the proton, GeV\n",
"print'%s %.2f %s'%(\"\\nThe energy of the proton = \",E_p/1e+009,\" GeV\");\n",
"print(\"wrong answer in the textbook\")\n",
"## Result\n",
"## The energy of the proton = 1.92e+006 GeV \n",
"## Wrong answer given in the textbook"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"The energy of the proton = 1918976.54 GeV\n",
"wrong answer in the textbook\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}