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diff --git a/Nuclear_Physics_by_D_C_Tayal/11-Particle_Accelerators.ipynb b/Nuclear_Physics_by_D_C_Tayal/11-Particle_Accelerators.ipynb new file mode 100644 index 0000000..74f6461 --- /dev/null +++ b/Nuclear_Physics_by_D_C_Tayal/11-Particle_Accelerators.ipynb @@ -0,0 +1,457 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 11: Particle Accelerators" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.10: Electrons_accelerated_in_electron_synchrotron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.10 : : Page-538 (2011)\n", +"clc; clear;\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*%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", +" printf('\nThe frequency of the applied electric field = %5.3e cycles per sec \nThe magnetic field intensity = %4.3f tesla\nThe energy radiated by the electron = %3.1f eV', f, B, del_E);\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 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.11: Kinetic_energy_of_the_accelerated_nitrogen_ion.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.11 : : Page-538 (2011)\n", +"clc; clear;\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 = 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 = sqrt(P_n^2+(0.938*14)^2)-0.938*14; // Kinetic energy of the accelerated nitrogen ion\n", +" printf('\nThe kinetic energy of the accelerated nitrogen ion = %4.2f MeV', T_n);\n", +"// Result\n", +"// The kinetic energy of the accelerated nitrogen ion = 8.43 MeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.12: EX11_12.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.12 : : Page-539 (2011)\n", +"clc; clear;\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 (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*%pi*R*10^6); // Frequency of the circular orbit, mega cycles per sec\n", +"f_0 = 2*%pi*R*f_c*10^3/(2*%pi*R+4*L); // Reduced frequency, kilo cycles per sec\n", +"B_m = 3.33*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*%pi*R+4*L)*(T+m_0_c_sq)*e*1e+015); // Maximum frequency of the accelerating voltage, mega cycles per sec\n", +" printf('\nThe maximum magnetic flux density = %5.3f weber/Sq.m\nThe maximum frequency of the accelerating voltage = %4.2f MHz', B_m, f_0);\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 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.13: Energy_of_the_single_proton_in_the_colliding_beam.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.13 : : Page-539 (2011)\n", +"clc; clear;\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", +"printf('\nThe energy of the proton = %5.2e GeV', E_p/1e+009);\n", +" \n", +"// Result\n", +"// The energy of the proton = 1.92e+006 GeV \n", +"// Wrong answer given in the textbook" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.14: Energy_of_the_electron_during_boson_production.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.14 : : Page-539 (2011)\n", +"clc; clear;\n", +"M_z = 92; // Mass of the boson,giga electron volts\n", +"E_e = M_z/2; // Energy of the electron,giga electron volts\n", +"c = 3e+08; // Velocity of the light, metre per second\n", +"m_e = 9.1e-31*c^2/(1.6e-019*1e+009); // Mass of electron, giga electron volts\n", +"E_e_plus = M_z^2/(2*m_e); // Threshold energy for the positron, giga electron volts \n", +" printf('\nThe energy of the electron = %d GeV\nThe threshold energy of the positron = %4.2e GeV', E_e, E_e_plus);\n", +" \n", +"// Result\n", +"// The energy of the electron = 46 GeV\n", +"// The threshold energy of the positron = 8.27e+006 GeV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.1: Optimum_number_of_stages_and_ripple_voltage_in_Cockcroft_Walton_accelerator.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.1 : : Page-535(2011) \n", +"clc; clear;\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 = sqrt (V_0*f*C/I); // Number of particles\n", +"delta_V = I*n*(n+1)/(4*f*C);\n", +"printf('\nThe optimum number of stages in the accelerator = %d', n);\n", +"printf('\nThe ripple voltage = %4.1f kV', delta_V/1e+003);\n", +"// Result\n", +"// The optimum number of stages in the accelerator = 10\n", +"// The ripple voltage = 27.5 kV " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.2: Charging_current_and_potential_of_an_electrostatic_generator.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.2 : : Page-536 (2011)\n", +"clc; clear;\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", +"printf('\nThe charging current = %d micro-ampere \nThe rate of rise of electrode potential = %4.2f MV/sec', i, V);\n", +"// Result\n", +"// The charging current = 239 micro-ampere \n", +"// The rate of rise of electrode potential = 2.15 MV/sec " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.3: Linear_proton_accelerator.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.3 : : Page-536 (2011)\n", +"clc; clear;\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*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", +"L = 1/f*sqrt(2*q*V/M)*integrate('n^(1/2)', 'n', 0, N); // Total length of the accelerator, metre\n", +"printf('\nThe length of the final drift tube = %d cm\nThe kinetic energy of the injected protons = %4.2f MeV\nThe total length of the accelerator = %3.1f metre', L_f, K_E, L);\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 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.5: Energy_and_the_frequency_of_deuterons_accelerated_in_cyclotron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.5 : : Page-536 (2011)\n", +"clc; clear;\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*%pi*M_d)*10^-6; // Frequency of the deutron voltage, mega cycles per sec\n", +"B_He = 2*%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", +"printf('\nThe energy of the emerging deutron = %4.1f MeV\nThe frequency of the dee voltage = %5.2f MHz\nThe change in magnetic field = %4.2f tesla', E, f, B_change);\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 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.6: Protons_extracted_from_a_cyclotron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.6: : Page-537 (2011)\n", +"clc; clear;\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 = 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", +" printf('\nThe effective reduction in magnetic field = %5.3f tesla \nThe change in orbit radius = %5.3f metre ', B_red, r_change);\n", +"// Result\n", +"// The effective reduction in magnetic field = 0.132 tesla \n", +"// The change in orbit radius = 0.087 metre " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.7: Energy_of_the_electrons_in_a_betatron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.7 : : Page-537 (2011)\n", +"clc; clear;\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*%pi*f*R); // Total number of revolutions\n", +"Avg_E_per_rev = E*1e+006/N; // Average energy gained per revolution, electron volt\n", +"printf('\nThe energy of the electron = %4.1f MeV\nThe average energy gained per revolution = %6.2f eV', E, Avg_E_per_rev);\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" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.8: Electrons_accelerated_into_betatron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.8 : : Page-537 (2011)\n", +"clc; clear;\n", +"R = 0.35; // Orbit radius, metre\n", +"N = 100e+06/480; // Total number of revolutions\n", +"L = 2*%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", +" printf('\nThe peak current = %3.1e ampere \nThe average current = %4.2e ampere \nThe duty cycle = %3.1e', I_p, I_avg, tau);\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 " + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11.9: Deuterons_accelerated_in_synchrocyclotron.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"// Scilab code Exa11.9 : : Page-538 (2011)\n", +"clc; clear;\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*%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*%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", +" printf('\nThe maximum frequency of the dee voltage = %5.2f MHz\nThe kinetic energy of the deuteron = %5.1f MeV', f_max, K_E);\n", +" \n", +"// Result\n", +"// The maximum frequency of the dee voltage = 11.44 MHz\n", +"// The kinetic energy of the deuteron = 171.6 MeV " + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |