{ "cells": [ { "cell_type": "markdown", "id": "256b6cbe", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# The Parker Spiral with Python" ] }, { "cell_type": "markdown", "id": "0b3ad785", "metadata": { "editable": true, "slideshow": { "slide_type": "" } }, "source": [ "In this post, we will explore the numerical solution to the first-order nonlinear differential equation that models the solar wind speed as a function of the heliocentric distance. Once this velocity profile is obtained, which is temperature-dependent, we proceed to transform it into Lagrangian coordinates centered at an emission point on the corona. This will make it more natural to construct an arm of the Parker spiral, along which the found velocity profile evolves." ] }, { "cell_type": "markdown", "id": "d417a2a1", "metadata": {}, "source": [ "When we talk about the \"Parker spiral\", we refer to the shape of the Sun's magnetic field in our solar system as a result of its rotation and the magnetohydrodynamic interaction with the expanding solar wind. This generates a swirling shape in the description of the magnetic field, which we will see how to obtain using Python." ] }, { "cell_type": "markdown", "id": "c3181800", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Solar wind" ] }, { "cell_type": "markdown", "id": "55109d3e", "metadata": {}, "source": [ "[Solar wind](https://en.wikipedia.org/wiki/Solar_wind) is a flow of charged particles (mainly electrons $e^-$, protons $p^+$ and alpha particles $\\alpha$), emitted from the solar atmosphere. These charged particles (ionized gas or plasma), escape the gravitational attraction of the Sun due to their high kinetic energy resulting from the temperature of the corona solar and interaction with the magnetic field.\n", "\n", "The first mentions of its existence date back to Biermann in the 1950s, who through the observation of comet tails (in the opposite direction of the sun), suggested that there should be a flow of gas towards the outside of the Sun in a radial direction. Parker takes this observation and assumes the Sun as a gravitating mass with spherical symmetry in expansion stationary (with the aim to ensure zero pressure condition at infinite distance) and initially disregarding the effects of the magnetic field. With these considerations, it is possible to manifest the dynamics of the flow of charged particles towards the outside of the Sun (Parker, 1958)." ] }, { "cell_type": "markdown", "id": "1d0a9143", "metadata": { "editable": true, "slideshow": { "slide_type": "" } }, "source": [ "## Solar Wind Velocity Profile\n", "\n", "In Parker's work under conditions of isothermal expansion ($\\gamma = 1$) of a neutral fluid (first approximation to the behavior of the solar wind), it leads to a non-linear first-order differential equation that relates the solar wind speed ($u(r)$) and the heliocentric distance ($r$). (Parker, 1958), (Kivelson, 1995)\n", "\n", "\\begin{equation}\n", "\\frac{du(r)}{dr} = \\left(\\frac{4kT}{mr} - \\frac{GM}{r^2} \\right)u(r)\\left(u(r)^2 - \\frac{2kT}{m} \\right)^{-1}\n", "\\end{equation}\n", "\n", "In order to reduce the propagation of errors due to orders of magnitude of the variables involved, the differential equation is adimensionalized based on the radius and velocity at the critical point (sonic point) (Piso, 2008).\n", "\n", "\\begin{eqnarray}\n", "c_s^2 & = & \\frac{2kT}{m}\\\\\n", "r_c &=& \\frac{GM}{2c_s^2}\\\\\n", "\\frac{dv}{dR} &=& \\frac{2\\left(\\frac{1}{R} - \\frac{1}{R^2}\\right)}{v - \\frac{1}{v}}\n", "\\end{eqnarray}\n", "\n", "Where $v$ is the speed at sonic velocities ($c_s$) and $R$ is the radius at sonic radii ($r_c$). We observe that around the sonic radius and speed, there is a critical point that must be satisfied to ensure the physical meaning of the solution. Also, we have to note that this equation represents a boundary value problem, and in this case, the boundary condition of the problem in adimensional units is $v(R_{\\text{sun}}) = v_0$, where $R_{\\text{sun}}$ is the radius of the Sun, and it is the position from which the flow of particles begins to move with an initial speed $v_0$ that depends on the density of particles and temperature.\n", "\n", "The generation of the Parker spiral is due to the rotation of the Sun, so we apply the transformation of coordinates Lagrangian for rotating systems, leading to the differential equation:\n", "\\begin{equation}\n", "\\frac{d\\varphi}{dR} = \\frac{-\\omega}{v(R)}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "c3720afb", "metadata": {}, "source": [ "## Analytical and numerical solution to Parker equation with Python\n", "\n", "This equation can be solved analytically because the equation allows for separation of variables and by integration to find the implicit solution. We can use [SymPy](https://www.sympy.org/), a free and open-source computational algebra package available in Python (an alternative to commercial packages such as Maple and Mathematica).\n", "\n", "Regarding numerical solutions, we will implement the method of [Runge-Kutta 4 (RK4)](https://en.wikipedia.org/wiki/Runge%E2%80%93Kutta_method#Fourth_order_Runge%E2%80%93Kutta_methods), and for the angular component solution, we will do it simply with the [Euler's method](https://en.wikipedia.org/wiki/Euler_method) since this avoids having to interpolate the radial velocity solution to find intermediate points required by RK4. To implement this, we will need to manage arrays, and that's what we'll use with [NumPy](https://numpy.org/). Of course, we want to visualize the solution so we can understand it, so we'll use [Matplotlib](https://matplotlib.org/).\n", "\n", "So, let's install, in this case, with UV's help, [which is a faster alternative to pip and venv](project:/en/blog/2024/uv-alternativa-rapida-a-pip-y-venv.md). The `!` symbol is because it's a Notebook cell, but if you're in the terminal, you can omit it." ] }, { "cell_type": "code", "execution_count": 1, "id": "3e593e66", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[2mUsing Python 3.12.7 environment at: /home/cosmoscalibur/Documentos/git/cosmoscalibur.github.io/.venv\u001b[0m\n", "\u001b[2K\u001b[2mResolved \u001b[1m13 packages\u001b[0m \u001b[2min 515ms\u001b[0m\u001b[0m \u001b[0m\n", "\u001b[2K\u001b[2mInstalled \u001b[1m2 packages\u001b[0m \u001b[2min 77ms\u001b[0m\u001b[0m \u001b[0m\n", " \u001b[32m+\u001b[39m \u001b[1mmpmath\u001b[0m\u001b[2m==1.3.0\u001b[0m\n", " \u001b[32m+\u001b[39m \u001b[1msympy\u001b[0m\u001b[2m==1.13.3\u001b[0m\n" ] } ], "source": [ "!uv pip install matplotlib numpy sympy" ] }, { "cell_type": "markdown", "id": "d80c0ac4", "metadata": {}, "source": [ "We start by importing the necessary elements we will need. Each line is commented to explain why we require it, making its use clear." ] }, { "cell_type": "code", "execution_count": 2, "id": "8092b969", "metadata": {}, "outputs": [], "source": [ "from math import cos, pi, sin # Required for polar transformation to illustrate solution of spiral\n", "\n", "from IPython.display import display\n", "# To include graphics in the Notebook instead of pop-up windows\n", "#%matplotlib inline\n", "import matplotlib.pyplot as plt # Plotting library for numerical arrays\n", "from numpy import array, ones # Numerical arrays and a fixed value array\n", "from sympy import (\n", " dsolve, # Solver for ordinary differential equations\n", " Eq, # Allows setting up equations\n", " Function, # Declares variables that represent functions\n", " init_printing, # Initializes display options for notebooks\n", " plot_implicit, # Enables plotting of implicit functions\n", " solve, # Solution to algebraic equations\n", " symbols # Declares general symbols\n", ")\n", "init_printing() # Initializes printing session in the Notebook" ] }, { "cell_type": "markdown", "id": "f5c90d8a", "metadata": {}, "source": [ "### Analytical solution using SymPy\n", "\n", "The first step is to declare the required symbols. This is the function for speed profile and the symbol for distance from the center of the Sun. The functions are declared with `Function` and variables with `symbols`. In both cases, the argument is a string representing the letter that corresponds to the symbol, and we assign it to a Python variable with the same letter.\n", "\n", "Additionally, we will set up the equation that we previously obtained in adimensional form. We need to take into account that speed is a function, so we write it as usual, indicating its form with parentheses and the variable it depends on, $v(R)$. To express the derivative, SymPy supports the method `.diff` whose argument is the variable with respect to which we differentiate. In this case, we would set up as `v(R).diff(R)`." ] }, { "cell_type": "code", "execution_count": 3, "id": "eb4b0365", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{d}{d R} v{\\left(R \\right)} = \\frac{\\frac{2}{R} - \\frac{2}{R^{2}}}{v{\\left(R \\right)} - \\frac{1}{v{\\left(R \\right)}}}$" ], "text/plain": [ " 2 2 \n", " ─ - ── \n", " R 2 \n", "d R \n", "──(v(R)) = ───────────\n", "dR 1 \n", " v(R) - ────\n", " v(R)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = Function('v') # Define speed function\n", "R = symbols('R') # Define distance variable\n", "# Specify differential equation\n", "eq_ord = Eq(v(R).diff(R), 2*(1/R - 1/R**2)/(v(R) - 1/v(R)))\n", "eq_ord" ] }, { "cell_type": "markdown", "id": "ebf7ed28", "metadata": {}, "source": [ "SymPy supports the method of separation of variables. If we need a specific form or want to hint to the algorithm, we can add an option that recommends the method. In this case, it would be `hint='separable'`. However, since our case is not separable, we don't use this option.\n", "\n", "For our specific problem, it's essential to indicate the method so that later the option of no simplification will show us the typical equation described in Parker's article. The function for solving ordinary differential equations is `dsolve`." ] }, { "cell_type": "code", "execution_count": 4, "id": "924212a1", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\frac{v^{2}{\\left(R \\right)}}{2} - \\log{\\left(v{\\left(R \\right)} \\right)} = C_{1} + 2 \\log{\\left(R \\right)} + \\frac{2}{R}$" ], "text/plain": [ " 2 \n", "v (R) 2\n", "───── - log(v(R)) = C₁ + 2⋅log(R) + ─\n", " 2 R" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Apply separable variable method\n", "# Not simplify to show implicit form\n", "sol_impl = dsolve(eq_ord, hint='separable', simplify=False)\n", "sol_impl" ] }, { "cell_type": "markdown", "id": "a4d47713", "metadata": {}, "source": [ "For curious readers, we can also allow the solution to be simplified and obtain an explicit form that depends on the [Lambert W function](https://en.wikipedia.org/wiki/Lambert_W_function). This is not the usual form in which the solution will be referenced, but thanks to computer algebra systems, we can dispense with this since the 1990s. To do so, we can remove the option of no simplification, and also if we remove the method recommendation, we will also obtain the Lambert W function." ] }, { "cell_type": "code", "execution_count": 5, "id": "16dc776d", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle v{\\left(R \\right)} = \\frac{e^{- C_{1} - \\frac{W\\left(- \\frac{e^{- 2 C_{1} - \\frac{4}{R}}}{R^{4}}\\right)}{2} - \\frac{2}{R}}}{R^{2}}$" ], "text/plain": [ " ⎛ 4 ⎞ \n", " ⎜ -2⋅C₁ - ─ ⎟ \n", " ⎜ R ⎟ \n", " ⎜-ℯ ⎟ \n", " W⎜────────────⎟ \n", " ⎜ 4 ⎟ \n", " ⎝ R ⎠ 2\n", " -C₁ - ─────────────── - ─\n", " 2 R\n", " ℯ \n", "v(R) = ──────────────────────────\n", " 2 \n", " R " ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dsolve(eq_ord)" ] }, { "cell_type": "markdown", "id": "65a932be", "metadata": {}, "source": [ "To determine which values of the constant of integration to use, we need to consider that the solution must satisfy passing through the critical point. Therefore, by assigning a value to the critical point, we can solve for the constant. To make this substitution, we use the method `.subs`, which takes a dictionary where keys are original symbols and values are new values or symbols." ] }, { "cell_type": "code", "execution_count": 6, "id": "fce2328f", "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[ - \\frac{3}{2}\\right]$" ], "text/plain": [ "[-3/2]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(sol_impl.subs({v(R): 1, R: 1}))" ] }, { "cell_type": "markdown", "id": "ebd6b714", "metadata": {}, "source": [ "To plot the solution, we need to replace the velocity function with a symbol and proceed with changes of the constant of integration to generate the family of solutions. Since we already know that for passing through the critical point, the constant must be $-3/2$, we will use this value, but also need an upper bound (e.g., $1$) and a lower bound (e.g., $2$). To graph the implicit function, we will use SymPy's `plot_implicit` method, which creates a grid of points in the plane of interest to evaluate if the equality holds. We will use `show=False` so that each curve is not shown separately, allowing us to add all three scenarios in one plot." ] }, { "cell_type": "code", "execution_count": 7, "id": "b9ccfada", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "V = symbols('V') # Define velocity variable\n", "# Implicit plot to 3 values of constant integration\n", "# show=False to manipulate plot as unique canvas\n", "p1 = plot_implicit(\n", " sol_impl.subs({'C1': -1, v(R): V}),\n", " (R, 0, 5),\n", " (V, 0, 5),\n", " line_color='green',\n", " show=False\n", ")\n", "p2 = plot_implicit(\n", " sol_impl.subs({'C1': -2, v(R): V}),\n", " (R, 0, 5),\n", " (V, 0, 5),\n", " line_color='blue',\n", " show=False\n", ")\n", "p3 = plot_implicit(\n", " sol_impl.subs({'C1': -1.5, v(R): V}),\n", " (R, 0, 5),\n", " (V, 0, 5),\n", " line_color='red',\n", " show=False\n", ")\n", "p1.extend([p2[0], p3[0]]) # append curve plots to same axes\n", "p1.show() # Show plot" ] }, { "cell_type": "markdown", "id": "5180168e", "metadata": {}, "source": [ "The blue curves are referred to as Solutions I and II. They are solutions of double evaluation and therefore are not physically acceptable solutions. The rightmost blue curve (II) also does not start on the surface of the Sun, while the leftmost blue curve (I) makes no physical sense since it would escape from the Sun with a subsonic velocity and return with a supersonic velocity.\n", "\n", "The green curves (III - upper, IV - lower) are solutions that do not pass through the critical point and therefore are not physically acceptable. Additionally, Curve III starts with a supersonic velocity near the Sun, which has not been observed, while Curve IV leads to constant pressure in the interstellar medium, which makes no physical sense.\n", "\n", "In contrast, the red ascending curve (V) leads to an increase in velocity after the critical point, which is observed, but also leads to zero pressure in the interstellar medium. This is known as the solar wind solution.\n", "\n", ":::{attention}\n", "\n", "At the level of the graph, a dense zone is observed around the critical point, but this is an effect of the implicit plotting method used with adaptive rendering.\n", ":::" ] }, { "cell_type": "markdown", "id": "bc1f10d2", "metadata": {}, "source": [ "### Numerical solution\n", "\n", "It is observed that at the critical point $(r_c, c_s)$, there is an indeterminacy. For this reason, it is necessary to solve the differential equation before and after this point as two independent intervals. The first interval, to ensure its passage through the critical point, is recommended to be solved with a backward form, so that we can use this information as an initial condition in the differential equation instead of making an estimate of the initial conditions on the solar radius (which would be the same for both intervals).\n", "\n", "Therefore, we have to set $v(1) = 1$, for the first tramm that goes from the radius of the coronal solar up to the critical point, and the second interval that goes from the critical point to Earth (having a reference point for the solution going forward).\n", "\n", "We define the function for numerical values on the right-hand side of the differential equation ($\\frac{d}{dR}v(R)$) in `f_ode` and define our function for the RK4 method, `RK4`." ] }, { "cell_type": "code", "execution_count": 8, "id": "62626400", "metadata": {}, "outputs": [], "source": [ "def f_ode(R, v):\n", " # Derivative of velocity profile function\n", " return 2 * (1/R- 1/R**2)/(v-1/v)\n", "\n", "def RK4(funcion, cond_inicial, x_final, n):\n", " # RK4 solver\n", " x = [cond_inicial[0]]\n", " w = [cond_inicial[1]]\n", " dx = (x_final - x[0]) / n # step\n", " dx_2 = dx / 2 # half step\n", " for i in range(n-1):\n", " k1 = dx * funcion(x[i], w[i])\n", " k2 = dx * funcion(x[i] + dx_2, w[i] + k1/2)\n", " k3 = dx * funcion(x[i] + dx_2, w[i] + k2/2)\n", " x.append(x[i] + dx) # x[i+1] = x[-1]\n", " k4 = dx * funcion(x[-1], w[i] + k3)\n", " w.append(w[i] + (k1 + 2*k2 + 2*k3 + k4)/6)\n", " return x, w" ] }, { "cell_type": "markdown", "id": "7ff56d31", "metadata": {}, "source": [ "Define required constants and helper functions to compute sonic velocity and sonic radii." ] }, { "cell_type": "code", "execution_count": 9, "id": "ab17cc32", "metadata": {}, "outputs": [], "source": [ "G = 6.67e-11 #Nm2kg-2\n", "k = 1.38065e-23 #JK-1\n", "M = 1.988435e30 #kg, Sun mass\n", "m_H = 1.67372e-27 #kg, hydrogen mass\n", "r_max = 150e9 #m, Earth-Sun distance\n", "r_min = 695.5e6 #m, Sun radii\n", "omega_sol = 2.7e-6 #rads-1, Sun angular velocity\n", "T_cor = 1e6 #K, Corona temperature\n", "\n", "def c_s(T = T_cor, m = m_H):\n", " # Sonic velocity\n", " from math import sqrt\n", " return sqrt(2*k*T/m)\n", "\n", "def r_c(T = T_cor, m = m_H):\n", " # Sonic radii\n", " return G*M / (2 * c_s(T, m)**2)" ] }, { "cell_type": "markdown", "id": "d35cea0b", "metadata": {}, "source": [ "Define adiminensional parameters " ] }, { "cell_type": "code", "execution_count": 10, "id": "2d7a93cd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Sonic velocity: 128.444465km/s\n", "Sonic radii: 4019540.880399km\n", "Unit time: 31293.998427s\n", "omega (adim): 0.084494\n", "Max radii (adim): 37.317695\n", "Min radii (adim): 0.173030\n" ] } ], "source": [ "vel_s = c_s(T_cor, m_H)\n", "rad_s = r_c(T_cor, m_H)\n", "t_s = rad_s / vel_s\n", "print(\"Sonic velocity: {:f}km/s\".format(vel_s/1000))\n", "print(\"Sonic radii: {:f}km\".format(rad_s/1000))\n", "print(\"Unit time: {:f}s\".format(t_s))\n", "omega_s = omega_sol * t_s\n", "print(\"omega (adim): {:f}\".format(omega_s))\n", "R_max = r_max / rad_s\n", "R_min = r_min / rad_s\n", "print(\"Max radii (adim): {:f}\".format(R_max))\n", "print(\"Min radii (adim): {:f}\".format(R_min))" ] }, { "cell_type": "markdown", "id": "8a92856b", "metadata": {}, "source": [ "Now we apply the RK4 method for the segments and graph the results. It is important to note that since the first segment is reversed, in order to properly arrange the solution, we need to apply the reverse of the list (`.reverse`) and thus keep the solution ordered." ] }, { "cell_type": "code", "execution_count": 11, "id": "c4b207ac", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Numerical solution to solar wind equation\n", "R, v = RK4(f_ode, [1, 1-1e-6], R_min, 30000)\n", "R.reverse()\n", "v.reverse()\n", "R_sup, v_sup = RK4(f_ode, [1, 1+ 1e-6 ], R_max, 1000000)\n", "v.extend(v_sup)\n", "R.extend(R_sup)\n", "# Graficamos\n", "plt.plot(1, 1, 'or')\n", "plt.text(1.2, 1, 'Sonic point')\n", "plt.plot(R[-1], v[-1], 'og')\n", "plt.text(R[-1] + .2, v[-1]-.2,'Earth')\n", "plt.plot(R, v)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0a2baf82", "metadata": {}, "source": [ "Starting from this velocity profile, we construct the angular velocity component to ultimately generate the well-known Parker spiral, and we can do this using the Euler method." ] }, { "cell_type": "code", "execution_count": 12, "id": "da835729", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = len(R)\n", "cont = 0\n", "psi = [0]\n", "x = [R[0]*cos(psi[0])]\n", "y = [R[0]*sin(psi[0])]\n", "while cont < N-1:\n", " # Euler method\n", " dR = R[cont + 1] - R[cont]\n", " dpsi = -omega_s * dR / v[cont]\n", " psi.append(psi[-1] + dpsi)\n", " cont = cont + 1\n", "\n", "dpsi_v = ones([N]) * pi / 2\n", "psi1 = array(psi)\n", "psi2 = psi1 + dpsi_v\n", "psi3 = psi2 + dpsi_v\n", "psi4 = psi3 + dpsi_v\n", "espiral = plt.subplot(111, projection='polar')\n", "espiral.plot(psi1, R, color='r')\n", "espiral.plot(psi2, R, color='r')\n", "espiral.plot(psi3, R, color='r')\n", "espiral.plot(psi4, R, color='r')" ] }, { "cell_type": "markdown", "id": "6e2b0636", "metadata": {}, "source": [ "# Referencias \n", "\n", "- E. N. Parker, [\"Dynamics of the Interplanetary Gas and Magnetic Fields\"](https://articles.adsabs.harvard.edu/pdf/1958ApJ...128..664P), Astrophysical Journal, 128, 1958 p. 664. \n", "- Margaret G. Kivelson y Christopher T. Russel, \"Introduction to Space Physics\", Cambridge University Press, 1995, 588 p. \n", "- Ana Maria Piso, [\"The Solar Wind\" from Wolfram Demonstrations Project](http://demonstrations.wolfram.com/TheSolarWind/), Agosto 6 de 2008. \n", "- Richard L. Burden y J. Douglas Faires, \"Análisis Numérico\", 7Ed., Ediciones Paraninfo, 2002 p. 839. " ] } ], "metadata": { "category": "science, computational physics", "date": "2024-10-06", "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.12.7" }, "tags": "solar wind, numerical methods, rk4, python, sympy" }, "nbformat": 4, "nbformat_minor": 5 }