{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
" \n",
"\n",
"# Uniform Magnetic Field\n",
"\n",
"### Examples - Electromagnetism\n",
"\n",
"By Eilif Sommer Øyre, Niels Henrik Aase, Thorvald Ballestad, and Jon Andreas Støvneng\n",
" \n",
"Last edited: September 1st 2019\n",
"\n",
"___"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Introduction\n",
"\n",
"A charged particle moving in a magnetic field will experience a magnetic force governed by Lorentz force law. This force is always perpendicular to the direction of motion of the particle. If the particle moves in uniform magnetic field and the velocity of the particle is normal to the direction of the field, the particle end up moving in a circle. Now, if the direction of the field is not normal to the velocity, the particle starts moving in a helix, unless its motion is completely parallel to the field in which the there is no Lorentz force and the particle moves in a perfectly straight line. In this notebook we will try to simulate the two former scenarios by numerically integrate the particle's equations of motion using the Euler method."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Theory\n",
"### The Lorentz force law\n",
"A particle with charge $Q$ and mass $m_p$ moving with a velocity $\\mathbf{v}$ in a magnetic field $\\mathbf{B}$ experiences a force \n",
"\n",
"\\begin{equation}\n",
" \\mathbf{F}_{mag} = Q(\\mathbf{v} \\times \\mathbf{B})\n",
"\\label{Lorentz}\n",
"\\end{equation}\n",
"\n",
"known as the *Lorentz force* [[1]](#rsc). Here, bold symbols represent vectors while normal symbols represent scalars.\n",
"\n",
"### Discretisation\n",
"The Lorentz force can be written as a second order ordinary differential equation (ODE)\n",
"\n",
"\\begin{equation}\n",
"m_p\\frac{d^2\\mathbf{x}}{dt^2} = Q\\big(\\frac{d\\mathbf{x}}{dt} \\times \\mathbf{B}\\big),\n",
"\\label{LorentzODE}\n",
"\\end{equation}\n",
"\n",
"where the velocity components are written as the time derivative of the positional components $v_i = dx_i/dt$. The left hand side of the equation is of course Newton's second law, where $d^2\\mathbf{x}/dt^2$ is the acceleration of the particle written as the second derivative of the position with respect to time. By decomposing the vectors, \\eqref{LorentzODE} can be reduced into three sets of two first order ODE's.\n",
"\n",
"\\begin{equation}\n",
"\\begin{aligned}\n",
" &\\frac{dx}{dt} = v_x\\\\[4pt]\n",
" &\\frac{dv_x}{dt} = \\frac{Q}{m_{p}}(v_yB_z - v_zB_y)\\\\[10pt]\n",
" &\\frac{dy}{dt} = v_y\\\\[4pt]\n",
" &\\frac{dv_y}{dt}= \\frac{Q}{m_{p}}(v_zB_x - v_xB_z)\\\\[10pt]\n",
" &\\frac{dz}{dt} = v_z\\\\[4pt]\n",
" &\\frac{dv_z}{dt} = \\frac{Q}{m_{p}}(v_xB_y - v_yB_x) .\n",
"\\end{aligned}\n",
"\\label{LorentzComponents}\n",
"\\end{equation}\n",
"\n",
"Using a numerical method such as the Euler method or Runge-Kutta fourth order, we can find approximate solutions for the ODE using a specified time step, $\\Delta t$, and the motion of a charged particle in a magnetic field can be found.\n",
"\n",
"## Numerical validity\n",
"\n",
"### Conservation of energy\n",
"\n",
"Since the Lorentz force is a cross product between the particle's velocity and the magnetic field, its direction is always perpendicular to the velocity of the particle. Consequently, the Lorentz force does no work on the particle, and the particle's kinetic energy is conserved. A test for numerical validity is then to check the deviation in initial and final kinetic energy.\n",
"\n",
"### Larmor radius\n",
"\n",
"As stated in the introduction, a charged particle will move in a circle if it has a velocity component perpendicular to an external magnetic field. This is called Larmor gyration, and the gyroradius (or Larmor radius), the radius of the circle, is given by [[2]](#rsc)\n",
"\n",
"\\begin{equation}\n",
"r_L = \\frac{mv_{\\perp}}{|Q| B} ,\n",
"\\label{larmorRadius}\n",
"\\end{equation}\n",
"\n",
"where $v_{\\perp}$ is the velocity of the particle perpendicular to the magnetic field with magnitude $B$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Implementation"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# First, import all necessary library packages\n",
"import numpy as np # For math and array manipulation\n",
"import matplotlib.pyplot as plt # For plotting\n",
"from mpl_toolkits.mplot3d import Axes3D # For 3D-plotting\n",
"plt.style.use(\"bmh\") # Set a particular style on the plots\n",
"# \"Magic\" command to adapt matplotlib plots to jupyter notebook\n",
"%matplotlib inline \n",
"figsize = (6, 6) # Tuple tho hold figure size of plots\n",
"dpi = 100 # Dots per inch on plots (resolution)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A charged particle moving through a uniform magnetic field can easily be simulated using the Euler method with the equations \\eqref{LorentzComponents}. Click [here](https://nbviewer.jupyter.org/urls/www.numfys.net/media/notebooks/eulers_method.ipynb) for a notebook on Euler's method. Below we define a function for the right hand side of the equations in \\eqref{LorentzComponents}, as well as a function for one explicit Euler step, given the current position and velocity."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"def RHS(M, RHSargs):\n",
" \"\"\" Returns the right hand side of the sets of ordinary \n",
" differential equations.\n",
" Arguments:\n",
" M 1x6 array containing the position and\n",
" velocity of the particle in cartesian\n",
" coordinates.\n",
" RHSargs 1x5 array containing the arguments/variables\n",
" of the right hand side of the Lorentz force.\n",
" \"\"\"\n",
" x, y, z, vx, vy, vz = M\n",
" Q, mass, Bx, By, Bz = RHSargs\n",
" ddt_vx = Q/mass*(vy*Bz - vz*By)\n",
" ddt_vy = Q/mass*(vz*Bx - vx*Bz)\n",
" ddt_vz = Q/mass*(vx*By - vy*Bx)\n",
" ddt_x = vx\n",
" ddt_y = vy\n",
" ddt_z = vz\n",
" return ddt_x, ddt_y, ddt_z, ddt_vx, ddt_vy, ddt_vz\n",
"\n",
"\n",
"def eulerStep(M, dt, RHS, RHSargs):\n",
" \"\"\" Performs one step of the Euler method.\"\"\"\n",
" x, y, z, vx, vy, vz = M # Extract positional and velocity components from matrix\n",
" dx, dy, dz, dvx, dvy, dvz = RHS(M, RHSargs) # Calculate right hand side of ODE's\n",
" # Increment each component using Euler's method\n",
" x = x + dx*dt\n",
" y = y + dy*dt\n",
" z = z + dz*dt\n",
" vx = vx + dvx*dt\n",
" vy = vy + dvy*dt\n",
" vz = vz + dvz*dt\n",
" return x, y, z, vx, vy, vz"
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"For now, we want the particle to move in a uniform magnetic field with an initial velocity perpendicular to the field direction."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial to final energy deviation:\t\t2.020 percent\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Q = 1 # Particle charge\n",
"mass = 1 # Particle mass\n",
"Bx = 10 # Magnetic field x-component magnitude\n",
"By = 0 # Magnetic field y-component magnitude\n",
"Bz = 0 # Magnetic field z-component magnitude\n",
"h = 1e-4 # Time step for numerical integration\n",
"tMax = 2 # Total duration of integration\n",
"n = int(tMax/h) # Number of datapoints\n",
"\n",
"\n",
"# Array of arguments (parameters) to the RHS function\n",
"RHSargs = np.array([Q, mass, Bx, By, Bz])\n",
"\n",
"# Initialising data matrix\n",
"M = np.zeros((6, n))\n",
"\n",
"# Initial position and velocity components\n",
"x0 = 0 # x-component magnitude of positional vector\n",
"y0 = 0 # y-component magnitude of positional vector\n",
"z0 = 0 # z-component magnitude of positional vector\n",
"vx0 = 0 # x-component magnitude of velocity vector\n",
"vy0 = 10 # y-component magnitude of velocity vector\n",
"vz0 = 0 # z-component magnitude of velocity vector\n",
"M[:, 0] = np.array([x0, y0, z0, vx0, vy0, vz0]) # Storing the components in the data matrix\n",
"\n",
"# The matrix M will have the following form when completly filled with data:\n",
"# \n",
"# M[ROW, COLUMN]\n",
"#\n",
"# n COLUMNS \n",
"# -----------------------------------\n",
"# 6 | x0 x1 x2 ... x_n-2 x_n-1\n",
"# | y0 y1 y2 ... y_n-1 y_n-1\n",
"# R | z0 z1 z2 ... z_n-1 z_n-1\n",
"# O | vx0 vx1 vx2 ... vx_n-1 vx_n-1\n",
"# W | vy0 vy1 vy2 ... vy_n-1 vy_n-1\n",
"# S | vz0 vz1 vz2 ... vz_n-1 vz_n-1\n",
"# \n",
"# Writing \":\" in M[ROWS, COLUMNS] such as M[:, 0] returns an array containing\n",
"# the first column. M[0, :] returns the first row\n",
"#\n",
"\n",
"# Integrate particle trajectory\n",
"for i in range(n-1):\n",
" M[:, i+1] = eulerStep(M[:, i], h, RHS, RHSargs)\n",
" \n",
"# Calculating deviation in kinetic energy\n",
"# Check out scipy.org for a description of the numpy-function numpy.linalg.norm(),\n",
"# here we use it to calculate the absolute value of the velocity by squaring its components.\n",
"Ke_initial = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, 0], axis=0))**2 # mv^2/2 (formula for kinetic energy)\n",
"Ke_final = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, -1], axis=0))**2\n",
"energyDeviation = np.abs(Ke_final - Ke_initial)/Ke_initial*100\n",
"print(\"Initial to final energy deviation:\\t\\t%.3f percent\"%(energyDeviation))\n",
"\n",
"# Plot path\n",
"plt.figure(figsize=(6, 6), dpi=dpi)\n",
"plt.plot(M[1], M[2])\n",
"plt.xlabel('y', size=10)\n",
"plt.ylabel('z', size=10)\n",
"plt.title(\"Charged particle in uniform B-field\", size=10)\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The particle moves in a circle in the $yz$-plane, as expected by equation \\eqref{Lorentz}. Our parameters yields the Larmor radius $r_g = 1$ from equation \\eqref{larmorRadius}. By a quick look at the axis above it seems accurate. \n",
"\n",
"Concerning conservation of energy, we see that the kinetic energy deviate with $2\\%$ from its initial value, indicating that the time step was roughly appropriate for this integration interval. However, if integrating over a longer period (larger `tmax`), this deviation might grow to large because of the accumulating numerical error in each Euler step, and the numerical validity weakens. It may be wise to run a convergence test using different time steps and comparing the total error."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Creating an array of timeSteps with logarithmic spacing\n",
"timeSteps = np.logspace(-7, -2.5, 30)\n",
"# Array to hold deviations for each time step\n",
"deviations = np.zeros((len(timeSteps)))\n",
"\n",
"Ke_initial = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, 0], axis=0))**2\n",
"\n",
"for k in range(len(timeSteps)):\n",
" h = timeSteps[k]\n",
" n = int(tMax/h) # Number of datapoints\n",
" # Initialising data matrix\n",
" M = np.zeros((6, n))\n",
" M[:, 0] = np.array([x0, y0, z0, vx0, vy0, vz0]) # Storing the components in the data matrix\n",
"\n",
" # Integrate particle trajectory\n",
" for i in range(n-1):\n",
" M[:, i+1] = eulerStep(M[:, i], h, RHS, RHSargs)\n",
"\n",
" # Calculating deviation in kinetic energy\n",
" Ke_final = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, -1], axis=0))**2\n",
" energyDeviation = np.abs(Ke_final - Ke_initial)/Ke_initial*100\n",
" deviations[k] = energyDeviation\n",
"\n",
"plt.figure(figsize=(8, 4), dpi=dpi)\n",
"plt.loglog(timeSteps, deviations)\n",
"plt.xlabel('time step, [s]')\n",
"plt.ylabel('Initial to final energy deviation, percent')\n",
"plt.title('Numerical convergence test')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From the plot above we see that the error in kinetic velocity is first order in the time step $\\Delta t$. This result also indicate that a time step below $10^{-5}\\mathrm{s}$ is sufficient to get a deviation below $0.1\\%$.\n",
"\n",
"Now, how does the particle's trajectory look if the initial velocity is in both $x$ and $y$ direction?"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Initial to final energy deviation:\t\t0.100 percent\n"
]
},
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"vx0 = 10 # Resetting vx0 to 10\n",
"h = 1e-5\n",
"n = int(tMax/h) # Recalculating number of datapoints\n",
"M = np.zeros((6, n)) # Re-initialising data matrix\n",
"M[:, 0] = np.array([x0, y0, z0, vx0, vy0, vz0])\n",
"\n",
"for i in range(n-1):\n",
" M[:, i+1] = eulerStep(M[:, i], h, RHS, RHSargs)\n",
"# Calculating deviation in kinetic energy\n",
"Ke_initial = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, 0], axis=0))**2 # mv^2/2 (formula for kinetic energy)\n",
"Ke_final = 0.5*mass*np.absolute(np.linalg.norm(M[3:6, -1], axis=0))**2\n",
"energyDeviation = np.abs(Ke_final - Ke_initial)/Ke_initial*100\n",
"print(\"Initial to final energy deviation:\\t\\t%.3f percent\"%(energyDeviation))\n",
" \n",
"fig = plt.figure(figsize=(6,6), dpi=100)\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"# Plotting guiding line\n",
"ax.plot(M[0], M[0]*0, np.ones(len(M[0]))*-1, '--', linewidth=1)\n",
"# Plotting particle path\n",
"ax.plot(M[0], M[1], M[2])\n",
"ax.set_xlabel(r\"$x$\")\n",
"ax.set_ylabel(r\"$y$\")\n",
"ax.set_zlabel(r\"$z$\")\n",
"ax.set_title(\"Charged particle in uniform B-field\")\n",
"\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We get a helical motion! The velocity in $x$-direction is unchanged as consequence of the cross-product in the Lorentz force law. The blue line is the movement of the centre of Larmor gyration. This is called the guiding centre."
]
},
{
"cell_type": "markdown",
"metadata": {
"collapsed": true
},
"source": [
"___\n",
" \n",
"## Resources and Further Reading\n",
"[1] : Chen, F. 1984, Introduction to plasma physics and controlled fusion. Volume 1: Plasma physics (New York: Plenum Press) \n",
"[2] : [Bittencourt, J. 2004, Fundamentals of plasma physics (New York: Springer-Verlag)](http://home.zcu.cz/~kozakt/MPPL/literatura/Bittencourt%20-%20Fundamentals%20of%20Plasma%20Physics.pdf) "
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}