{ "cells": [ { "cell_type": "markdown", "id": "256b6cbe", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# Espiral de Parker con Python" ] }, { "cell_type": "markdown", "id": "0b3ad785", "metadata": { "editable": true, "slideshow": { "slide_type": "" } }, "source": [ "En esta entrada veremos la solución numérica a la ecuación diferencial no lineal de primer orden que modela la velocidad del viento solar en función de la distancia heliocéntrica. Una vez se obtiene este perfil de velocidad, el cual es dependiente de la temperatura se procede a transformar a coordenadas lagrangianas centradas en un punto de emisión sobre la corona. De esta forma será más natural construir un brazo de la espiral de Parker, sobre el cual evoluciona el perfil de velocidad hallado." ] }, { "cell_type": "markdown", "id": "d417a2a1", "metadata": {}, "source": [ "Cuando hablamos de la \"espiral de Parker\" nos referimos a la forma del campo magnético del Sol en nuestro sistema solar a raíz de su rotación y la interacción magnetohidrodinámica con el viento solar en expansión. Esto genera una forma de remolino en la descripción del campo magnético y es la que veremos como obtener con Python." ] }, { "cell_type": "markdown", "id": "c3181800", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "## Viento solar" ] }, { "cell_type": "markdown", "id": "55109d3e", "metadata": {}, "source": [ "El [viento solar](https://es.wikipedia.org/wiki/Viento_solar) es un flujo de partículas con carga eléctrica (en su mayoría, electrones $e^-$, protones $p^+$ y partículas alfa $\\alpha$), emanadas desde la atmósfera solar. Estas particulas cargadas (gas ionizado o plasma), escapan de la atracción gravitacional del Sol por su alta energía cinética resultado de la temperatura de la corona solar y de la interacción con el campo magnético. \n", "\n", "Las primeras menciones a su existencia corresponden a Biermann en los años 50, quien mediante la observación de la cola de los cometas (en dirección opuesta al sol), sugirió que debía existir un flujo de gas hacia afuera del Sol de forma radial. Parker toma esta observación, y asume el Sol como una masa gravitacional con simetría esférica en expansión estacionaria (con el fin de asegurar la condición de presión cero a distancia infinita) e inicialmente despreciando los efectos del campo magnético. Con estas consideraciones, se logra manifestar la dinámica del flujo de partículas hacia afuera del Sol (Parker, 1958)." ] }, { "cell_type": "markdown", "id": "1d0a9143", "metadata": { "editable": true, "slideshow": { "slide_type": "" } }, "source": [ "## Perfil de velocidad del viento solar \n", "\n", "En el trabajo de Parker bajo condiciones de expansión isotérmica ($\\gamma = 1$) de un fluido neutro (primera aproximación al comportamiento del viendo solar), lleva a una ecuación diferencial no lineal de primer orden que relaciona la velocidad del viento solar ($u(r)$) y la distancia heliocéntrica ($r$) ((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", "Con el fin de reducir la propagación de error por los ordenes de magnitud de las variables involucradas, se procede a adimensionalizar la ecuación diferencial, con base al radio y velocidad en el punto crítico (punto sónico) (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", "Donde $v$ es la velocidad en velocidades sónicas ($c_s$) y $R$ es el radio en radios sónicos ($r_c$). Observamos que alrededor del radio sónico y de la velocidad sónica se presenta un punto crítico que debe satisfacerse para asegurar el sentido físico de la solución. También, tenemos que esta ecuación representa un problema de valores de frontera, y en este caso la condición de frontera del problema en unidades adimensionales es $v(R_{sol}) = v_0$, donde $R_{sol}$ es el radio del Sol, y es la posición desde la cuál comienza a desplazarse el flujo de partículas con una velocidad inicial $v_0$ que dependerá de la densidad de partículas y la temperatura. \n", " \n", "La generación de la espiral de Parker es efecto de la rotación del sol, por lo cual se aplica la transformación de coordenadas lagrangianas para sistemas rotantes, llevando a la ecuación diferencial\n", "\\begin{equation}\n", "\\frac{d\\varphi}{dR} = \\frac{-\\omega}{v(R)}\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "c3720afb", "metadata": {}, "source": [ "## Solución analítica y numérica con Python\n", "\n", "Esta ecuación se puede solucionar analíticamente ya que la ecuación permite separación de variables y mediante integración encontrar la solución implícita. Podemos usar [SymPy](https://www.sympy.org/es/), un paquete de álgebra computacional de código abierto y libre, disponible en Python (una alternativa a paquetes comerciales como Maple y Mathematica). \n", "\n", "Respecto a la solución numérica, implementaremos el método de [Runge-Kutta 4 (RK4)](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Runge-Kutta#M%C3%A9todos_de_Runge-Kutta_de_cuarto_orden), y para la solución de la componente angular lo realizaremos de forma simple con el [método de Euler](https://es.wikipedia.org/wiki/M%C3%A9todo_de_Euler) ya que esto evita tener que interpolar la solución de velocidad radial para conocer puntos intermedios requeridos por RK4. Para su implementación vamos a necesitar el manejo de arreglos, y esto los usaremos con [NumPy](https://numpy.org/). Por supuesto, queremos ver gráficos para entender la solución, así que usaremos [Matplotlib](https://matplotlib.org/). \n", "\n", "Así que vamos a instalar, en este caso con la ayuda de UV, el cual es [una alternativa más rápida a _PIP_](project:/es/blog/2024/uv-alternativa-rapida-a-pip-y-venv.md). El `!` es porque es una celda de Notebook, pero si estás en la terminal, puedes omitirla. " ] }, { "cell_type": "code", "execution_count": 1, "id": "3e593e66", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\u001b[2mAudited \u001b[1m3 packages\u001b[0m in 2ms\u001b[0m\n" ] } ], "source": [ "!uv pip install matplotlib numpy sympy" ] }, { "cell_type": "markdown", "id": "d80c0ac4", "metadata": {}, "source": [ "Iniciamos con el bloque de importación de los elementos que vamos a necesitar. Cada línea se encuentra comentado con el motivo por el cual lo requerimos para que sea claro su uso." ] }, { "cell_type": "code", "execution_count": 2, "id": "8092b969", "metadata": {}, "outputs": [], "source": [ "from math import cos, pi, sin # Requerido para la transformación polar para ilustrar la solución de la espiral\n", "\n", "from IPython.display import display\n", "# Para incluir gráficos en el Notebook en lugar de ventanas emergentes\n", "#%matplotlib inline\n", "import matplotlib.pyplot as plt # Graficador para los arreglos numéricos\n", "from numpy import array, ones # Arreglos numéricos y el arreglo de unos\n", "from sympy import (\n", " dsolve, # Solucionador de ecuaciones diferenciales ordinarias\n", " Eq, # Permite plantear igualdades/ecuaciones\n", " Function, # Declara variables que representan funciones\n", " init_printing, # Inicializa la opción de visualización de ecuaciones\n", " plot_implicit, # Permite los gráficos de funciones implícitas\n", " solve, # Solución de ecuaciones algebraicas\n", " symbols # Declara símbolos generales\n", ")\n", "init_printing() # Inicializa sesión de impresión en el Notebook" ] }, { "cell_type": "markdown", "id": "f5c90d8a", "metadata": {}, "source": [ "### Solución analítica\n", "\n", "El primer paso es la declaración de los símbolos requeridos. Esto es la función del perfil de velocidad y el símbolo para la distancia al centro del sol. Las funciones se declaran con `Function` y las variables adicionales con `symbols`. En ambos casos, tenemos que el argumento es un _string_ de la letra que representa, y por convención lo asignamos a una variable Python con la misma letra. \n", "\n", "Adicional, vamos a plantear la ecuación que previamente obtuvimos para la forma adimensional, y debemos tener en cuenta que al ser la velocidad una función, se escribe como habitualmente se dispone, indicando su forma con paréntesis y la variable de la cual depende, $v(R)$. Y para expresar la forma de la derivada, las expresiones de SymPy suportan el método `.diff` cuyo argumento es la variable respecto a la cual se deriva. En este caso, se plantearía como `v(R).diff(R)`." ] }, { "cell_type": "code", "execution_count": 13, "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": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = Function('v') # Declara la función de velocidad\n", "R = symbols('R') # Declara la variable de distancia\n", "# Se plantea la ecuación diferencial\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 en los métodos soportados, dispone de la opción de separación de variables. Si necesitamos una forma particular o porque queremos dar un indicio al algoritmo, podemos añadir la opción que recomienda el método, en este caso sería `hint='separable'`. Para nuestro caso, es importante indicar el método para que luego la opción de no simplificación nos muestre la ecuación típica que se describe en el artículo de Parker. La función para la solución de ecuaciones diferenciales ordinarias, es `dsolve`." ] }, { "cell_type": "code", "execution_count": 14, "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": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Se aplica método de separación de variables\n", "# No se simplifica para mostrar la forma implícita\n", "sol_impl = dsolve(eq_ord, hint='separable', simplify=False)\n", "sol_impl" ] }, { "cell_type": "markdown", "id": "a4d47713", "metadata": {}, "source": [ "Solo para los curiosos, también podemos permitir que la solución sea simplificada y obtener la forma explícita, la cual depende de la [función Lambert W](https://es.wikipedia.org/wiki/Funci%C3%B3n_W_de_Lambert). Esta no es la forma usual en la cual encontraremos referenciada la solución, pero gracias a los sistemas de álgebra computacional podemos disponer de esta desde la década de los 90. Para ello podemos quitar la opción de no simplificar, pero también si removemos la recomendación de método, también la vamos a obtener." ] }, { "cell_type": "code", "execution_count": 15, "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": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dsolve(eq_ord)" ] }, { "cell_type": "markdown", "id": "65a932be", "metadata": {}, "source": [ "Ahora, para saber que valores de la constante de integración usar, debemos tener presente que la solución debe satisfacer pasar por el punto crítico, y por ende si asignamos el punto crítico, podemos despejar la constante. Para hacer la substitución usamos el método `.subs` que recibe un diccionario donde las llaves son los símbolos originales y los valores son los nuevos valores o símbolos." ] }, { "cell_type": "code", "execution_count": 16, "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": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solve(sol_impl.subs({v(R): 1, R: 1}))" ] }, { "cell_type": "markdown", "id": "ebd6b714", "metadata": {}, "source": [ "Para poder graficar, debemos reemplazar la función de velocidad de la función implícita por un símbolo, y proceder con los cambios de la constante de integración para generar la familia de soluciones. Como ya sabemos que para pasar por el punto crítico la constante debe ser $-3/2$, vamos a usar este valor, pero también necesitamos un valor superior (ejemplo, $1$), y un valor inferior (ejemplo, $2$). Para graficar al ser una función implícita, usaremos `plot_implicit` de SymPy que hace un mallado de puntos en el plano de interes para evaluar por celda el cumplimiento de la igualdad. Usaremos `show=False` para que no se muestre cada curva por separado y poder añadir los 3 escenarios en un mismo gráfico." ] }, { "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') # Símbolo para la velocidad\n", "# Graficamos implícitamente para 3 valores de la constante de integración\n", "# show=False es para no mostrar de una vez, y poder controlar el gráfico unido\n", "# extendiendo y mostrando a discreción\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]]) # Anexamos las curvas a la misma figura\n", "p1.show() # Se muestra la figura" ] }, { "cell_type": "markdown", "id": "5180168e", "metadata": {}, "source": [ "Las curvas azules son referenciadas como las soluciones I y II. Son soluciones de doble evaluación y por ende no son soluciones aceptables físicamente. La curva azul de la derecha (II) además no comienza en la superficie del sol. La curva azul izquierda (I) no hace sentido además porque escaparía del Sol con velocidad subsónica y se devolvería con velocidad supersónica. Las curvas verdes (III - superior, IV - inferior) son soluciones que no pasan por el punto crítico y por ende no son aceptables físicamente. Adicional la curva III inicia con velocidad supersónica en las proximidades del Sol y eso no se ha observado, y la curva IV lleva a una presión constante en el ambiente interestelar, por lo cual no tiene sentido físico. Por el contrario, la curva roja ascendente (V), lleva a un aumento a velocidad supersónica después del punto crítico, lo cual es observado, pero además, lleva a una presión cero en el ambiente interestelar. Esta es conocida como la solución del viento solar. \n", "\n", ":::{attention}\n", "\n", "A nivel del gráfico se observa una zona densa alrededor del punto crítico, pero esto es efecto del método de graficación implícito en modo adaptativo\n", ":::" ] }, { "cell_type": "markdown", "id": "bc1f10d2", "metadata": {}, "source": [ "### Solución numérica\n", "\n", "Se observa que en el punto crítico $(r_c, c_s)$, se presenta una indeterminación. Por este motivo, es necesario solucionar la ecuación diferencial antes y despues de este punto como dos tramos independientes. El tramo anterior, para asegurar su paso por el punto, lo recomendable es solucionarlo con una forma reversa (_backward_), de tal forma que se pueda usar esta información como condición inicial en la ecuación diferencial en lugar de hacer una estimación de las condiciones iniciales sobre el radio solar (y sería la misma en los dos tramos). \n", "Siendo así, tenemos que, $v(1) = 1$, para el primer tramo que va desde el radio de la corona solar hasta el punto crítico, y el segundo tramo que va desde el punto crítico hasta la Tierra (por tener un punto de referencia para la solución hacia adelante). \n", "\n", "Planteamos la función para los valores numéricos del lado derecho de la ecuación diferencial ($\\frac{d}{dR}v(R)$) en `f_ode` y planteamos nuestra función para el método RK4, `RK4`. " ] }, { "cell_type": "code", "execution_count": 8, "id": "62626400", "metadata": {}, "outputs": [], "source": [ "def f_ode(R, v):\n", " # Función de la derivada del perfil de velocidad respecto a la distancia\n", " return 2 * (1/R- 1/R**2)/(v-1/v)\n", "\n", "def RK4(funcion, cond_inicial, x_final, n):\n", " # Implementación del solucionador de Runge Kutta orden 4\n", " x = [cond_inicial[0]]\n", " w = [cond_inicial[1]]\n", " dx = (x_final - x[0]) / n # paso\n", " dx_2 = dx / 2 # medio paso\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": [ "Se definen las constantes requeridas y las funciones para calcular los radios y velocidades sonicas. " ] }, { "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, masa del sol\n", "m_H = 1.67372e-27 #kg, masa hidrogeno\n", "r_max = 150e9 #m, dist tierra-sol\n", "r_min = 695.5e6 #m, radio solar\n", "omega_sol = 2.7e-6 #rads-1, vel angular sol\n", "T_cor = 1e6 #K, temp corona solar\n", "\n", "def c_s(T = T_cor, m = m_H):\n", " # Velocidad sónica, la cual depende de la temperatura y densidad del medio\n", " from math import sqrt\n", " return sqrt(2*k*T/m)\n", "\n", "def r_c(T = T_cor, m = m_H):\n", " # Radio sónico\n", " return G*M / (2 * c_s(T, m)**2)" ] }, { "cell_type": "markdown", "id": "d35cea0b", "metadata": {}, "source": [ "Se determinan los parámetros en unidades adimensionales. " ] }, { "cell_type": "code", "execution_count": 10, "id": "2d7a93cd", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Velocidad sónica: 128.444465km/s\n", "Radio sónico: 4019540.880399km\n", "Unidad de tiempo: 31293.998427s\n", "omega (adim): 0.084494\n", "Radio máximo (adim): 37.317695\n", "Radio mínimo (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(\"Velocidad sónica: {:f}km/s\".format(vel_s/1000))\n", "print(\"Radio sónico: {:f}km\".format(rad_s/1000))\n", "print(\"Unidad de tiempo: {: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(\"Radio máximo (adim): {:f}\".format(R_max))\n", "print(\"Radio mínimo (adim): {:f}\".format(R_min))" ] }, { "cell_type": "markdown", "id": "8a92856b", "metadata": {}, "source": [ "Ahora aplicamos el método RK4 para los tramos y gráficamos. Es necesario tener presente que al estar reverso el primer tramo, también para disponer la solución hay que aplicar el reverso de la lista (`.reverse`) y así tener la solución ordenada. " ] }, { "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": [ "# Solución numérica de la ecuación de viento solar\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, 'Punto sónico')\n", "plt.plot(R[-1], v[-1], 'og')\n", "plt.text(R[-1] + .2, v[-1]-.2,'Tierra')\n", "plt.plot(R, v)\n", "plt.grid()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "0a2baf82", "metadata": {}, "source": [ "Partiendo de este perfil de velocidad se contruye la componente angular de la velocidad para generar finalmente la conocida espiral de Parker, y lo podemos hacer con el método de Euler. " ] }, { "cell_type": "code", "execution_count": 12, "id": "da835729", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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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", " # Método de Euler\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. " ] }, { "cell_type": "code", "execution_count": null, "id": "e0775621-a520-40c2-8aba-4abd39b70fe0", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "category": "ciencia, física computacional", "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": "3.10.12" }, "redirect": "es/blog/2024/espiral_de_parker", "tags": "viento solar, espiral de parker, método de runge kutta, python, sympy" }, "nbformat": 4, "nbformat_minor": 5 }