Plasma3_Last_HW.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Plasma3 Last HW",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyOelUEWTfeswooVud8ngyhq",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/erny123/HW/blob/main/Plasma3_Last_HW.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Ernesto Barraza-Valdez\n",
        "\n",
        "#Plasma 3-HW 9\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "6wgyQbBb0G8o"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1a)\n",
        "\n",
        "Given $\\omega_0$ we can write down the 5 equations for a parametric system: \n",
        "\n",
        "Manley Rowe:\n",
        "\n",
        "$\\omega_0 = \\omega_1 + \\omega_2 $\n",
        "\n",
        "$\\vec{k}_0 = \\vec{k}_1 + \\vec{k}_2 $\n",
        "\n",
        "Dispersions:\n",
        "\n",
        "$\\omega_0^2 = \\omega_p^2 + c^2 k_0^2 $\n",
        "\n",
        "$\\omega_1^2 = \\omega_p^2 + \\frac{3}{2} v_e^2 k_1^2 $\n",
        "\n",
        "$\\omega_2^2 = \\omega_p^2 + \\frac{3}{2} v_e^2 k_2^2 $\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n"
      ],
      "metadata": {
        "id": "h4j1XzSh0QV_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1b) \n",
        "\n",
        "given $v_e = 0.3 c$ and $\\omega_0 = \\sqrt{5} \\omega_p$ we can find $\\omega_1$ and $\\omega_1$ and corresponding wave vectors for a 1D system"
      ],
      "metadata": {
        "id": "6zDrQDhW1G-Y"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "87W5XkzmCLfO"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import matplotlib.colors as colors\n",
        "import matplotlib.ticker as plticker\n",
        "from matplotlib.ticker import FixedFormatter, FixedLocator\n",
        "plt.rcParams['figure.figsize'] = [6, 4]\n",
        "plt.rcParams['figure.dpi'] = 120 # 200 e.g. is really fine, but slower\n",
        "import random\n",
        "import pandas as pd\n",
        "from ipywidgets import interactive\n",
        "%matplotlib inline\n",
        "from sympy import *"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "q = 1.6*10**(-19)\n",
        "eps = 8.85e-12\n",
        "m = 9.1e-31\n",
        "amu = 1.66e-27\n",
        "mi = 12*amu\n",
        "c = 2.998e8\n",
        "kboltz = 1.38e-23\n",
        "kboltzKtoEV = 8.61e-5\n",
        "JtoeV = 1/(1.6e-19)\n",
        "ve = 0.3*c\n",
        "\n",
        "kp = np.arange(-3,3,0.1)\n",
        "#kp = np.linspace(-5, 5, 0.1)"
      ],
      "metadata": {
        "id": "-B-zAY9kCoMP"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w0 = Symbol('w0')\n",
        "w1 = Symbol('w1')\n",
        "w2 = Symbol('w2')\n",
        "k0 = Symbol('k0')\n",
        "k1 = Symbol('k1')\n",
        "k2 = Symbol('k2')"
      ],
      "metadata": {
        "id": "XRQ4qGZo1j5M"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "eq0 = sqrt(5) -sqrt(1+k0**2)\n",
        "eq1 = w1 - sqrt(1 + 3/2* 0.3**2 * k1**2)\n",
        "eq2 = w2 - sqrt(1 + 3/2* 0.3**2 * k2**2)\n",
        "eq3 = sqrt(5) - w1- w2\n",
        "eq4 = k0 - k1 - k2"
      ],
      "metadata": {
        "id": "TQIBt4lR1l1d"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "solve([eq0,eq1,eq2,eq3,eq4], (k0,w1,k1,w2,k2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aYalmyk71qYN",
        "outputId": "236e684b-02b4-400c-f6f5-c2a66bc1d72c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[(2.00000000000000,\n",
              "  1.00003497682122,\n",
              "  0.0227636594432406,\n",
              "  1.23603300067857,\n",
              "  1.97723634055676),\n",
              " (2.00000000000000,\n",
              "  1.23603300067857,\n",
              "  1.97723634055676,\n",
              "  1.00003497682122,\n",
              "  0.0227636594432406)]"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "w0 = np.sqrt(1 + kp**2)\n",
        "w1 = np.sqrt(1+3/2 * 0.3**2*kp**2)\n",
        "\n",
        "plt.plot(kp,w0,linewidth=3)\n",
        "plt.plot(kp,w1,linewidth=3)\n",
        "plt.arrow(0,0,2.0,np.sqrt(5),length_includes_head=True,width=0.05)\n",
        "plt.axhline(y=np.sqrt(5),color = 'r', linestyle = 'dashed' )\n",
        "plt.axhline(y=1,color = 'orange', linestyle = 'dashed' )\n",
        "plt.text(-3, np.sqrt(5)-0.25, '$\\sqrt{5} \\omega_p$', fontsize = 16, color='red')\n",
        "plt.arrow(0,0,0.02,1.0,length_includes_head=True,width=0.05)\n",
        "plt.arrow(0,0,1.98,1.24,length_includes_head=True,width=0.05)\n",
        "plt.ylim([0,2.5])\n",
        "plt.xlabel(\"$k/k_p$\",fontsize = 16)\n",
        "plt.ylabel(\"$\\omega/\\omega_p$\",fontsize = 16)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 311
        },
        "id": "Emk8X5xWDQqX",
        "outputId": "0b73f028-fa32-4e7d-8c4d-c1a046559bb4"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, '$\\\\omega/\\\\omega_p$')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1c)\n",
        "\n",
        "THe lowest frequencies for the plasmons is $\\omega_1 = \\omega_2 = \\omega_p$\n",
        "\n",
        "Thus \n",
        "\n",
        "$\\omega_0 = \\omega_1 + \\omega_2 = 2\\cdot \\omega_p$\n",
        "\n",
        "Is the lowest frequency possible for this decay instability. We convert the laser frequency to an equivalent critical density ($\\omega_0 → n_c$), and also the plasma frequency to an equivalent plasma density ($\\omega_p → n_e$) using $n = \\epsilon_0 m \\omega^2/e^2$:\n",
        "\n",
        "$n_c = 4\\cdot n_e → n_e = \\frac{1}{4}n_c$\n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "EzJwYYg82At0"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#1d)\n",
        "\n",
        "For a 351 nm Laser we have for $\\omega_0$"
      ],
      "metadata": {
        "id": "YS6FEofz3vyq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "wlaser = 2*np.pi * c/351e-9\n",
        "\n",
        "print(\"{:0.2e}\".format(wlaser))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "C7nYGdYt4VRJ",
        "outputId": "f0b60a11-742f-4c8b-f866-73f4c56a6f1e"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "5.37e+15\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Then the plasma density will have to be 1/4 the critical density or less:"
      ],
      "metadata": {
        "id": "oE-TlnP341DZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "ncrit = eps*m*wlaser**2 /q**2\n",
        "print(\"Critical Density = {:0.2e} /m^3\".format(ncrit))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "moMhlLjy4nHj",
        "outputId": "6825a03a-1135-42a3-b495-ad7cd4a41955"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Critical Density = 9.06e+27 /m^3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(\"1/4 Critical Density = {:0.2e} /m^3\".format(ncrit/4))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iMF04q7b5Lqc",
        "outputId": "62d9847e-0c1e-4c44-f1d7-567643655072"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1/4 Critical Density = 2.27e+27 /m^3\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Thus NIF laser will only see two-plasmon decay if the plasma target is has a density equal to or below $n_e = 2.27 \\times 10^{27} m^{-3}$"
      ],
      "metadata": {
        "id": "k2UF2d6i5hSf"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "wC2pZDhp5fvG"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}