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| author | hardythe1 | 2015-06-03 15:27:17 +0530 |
|---|---|---|
| committer | hardythe1 | 2015-06-03 15:27:17 +0530 |
| commit | 47d7279a724246ef7aa0f5359cf417992ed04449 (patch) | |
| tree | c613e5e4813d846d24d67f46507a6a69d1a42d87 /Nuclear_Physics/Chapter11.ipynb | |
| parent | 435840cef00c596d9e608f9eb2d96f522ea8505a (diff) | |
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diff --git a/Nuclear_Physics/Chapter11.ipynb b/Nuclear_Physics/Chapter11.ipynb new file mode 100755 index 00000000..ff1534f6 --- /dev/null +++ b/Nuclear_Physics/Chapter11.ipynb @@ -0,0 +1,572 @@ +{
+ "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": {}
+ }
+ ]
+}
\ No newline at end of file |