+{"nbformat_minor": 0, "cells": [{"execution_count": 9, "cell_type": "code", "source": "#Pkg.clone(\"https://github.com/jhlq/Equations.jl\")\n#Pkg.update()\nusing Equations\n\n#=\n \u03bbD is the Debye length, \n \u03b50 is the permittivity of free space, \n kB is Boltzmann's constant,\n qe is the charge on an electron, \n Te and Ti are the temperatures of the electrons and ions, respectively, multiplied by the Boltzmann's constant,\n ne is the density of electrons\n=#\n\nconstants=[:me\u22569.1094e-31,:qe\u22561.6022e-19,:kB\u22561.3807e-23,:\u03b50\u22568.8542e-12]\n\n# Solar wind\nne=:ne\u225610.0^7\nTe=:Te\u225610.0*:qe\nvariables=[ne,Te]\n# Debye length lD\nlD=:\u03bbD\u2256sqrt(:\u03b50*:Te/(:ne*:qe^2)) #valid when Te>>Ti\n# plasma frequency wp\nwp=:\u03c9p\u2256sqrt(:ne*:qe^2/(:\u03b50*:me))\n# particles in a debye cube ND\nND=:ND\u2256:ne*:\u03bbD^3\nprintln(lD&variables&constants)\nprintln(wp&lD&variables&constants)\nprintln(ND&lD&variables&constants)\n", "outputs": [{"output_type": "stream", "name": "stdout", "text": "\u03bbD \u2256 7.433892903446526\n\u03c9p \u2256 178400.95597166813\nND \u2256 4.108174668936227e9\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 10, "cell_type": "code", "source": "println(\"Lightning\")\nne.rhs=10.0^23\nprintln(lD&variables&constants)\nprintln(wp&lD&variables&constants)\nprintln(ND&lD&variables&constants)\nprintln(\"Magnetic fusion plasma\")\nne.rhs=10.0^20\nTe.rhs=10.0^4*:qe\nprintln(lD&variables&constants)\nprintln(wp&lD&variables&constants)\nprintln(ND&lD&variables&constants)\nprintln(\"Magnetic fusion plasma\")\nne.rhs=10.0^17\nTe.rhs=10.0^4*:kB\nprintln(lD&variables&constants)\nprintln(wp&lD&variables&constants)\nprintln(ND&lD&variables&constants)\n", "outputs": [{"output_type": "stream", "name": "stdout", "text": "Lightning\n\u03bbD \u2256 7.433892903446526e-8\n\u03c9p \u2256 1.7840095597166812e13\nND \u2256 41.08174668936228\nMagnetic fusion plasma\n\u03bbD \u2256 7.433892903446526e-5\n\u03c9p \u2256 5.641533576218887e11\nND \u2256 4.108174668936228e7\nMagnetic fusion plasma\n\u03bbD \u2256 2.1822655603609336e-5\n\u03c9p \u2256 1.784009559716681e10\nND \u2256 1039.2566127081407\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 11, "cell_type": "code", "source": "#parameters for solar core: ne=10^32, Te=10^7 => \u03bbD ~ 10^\u221211\nne.rhs=10.0^32\nTe.rhs=10.0^7*:kB\nprintln(lD&variables&constants)\nprintln(wp&lD&variables&constants)\nprintln(ND&lD&variables&constants)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "\u03bbD \u2256 2.1822655603609335e-11\n\u03c9p \u2256 5.641533576218887e17\nND \u2256 1.0392566127081406\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 12, "cell_type": "code", "source": "# Drifts\nve=:ve\u2256Cross(:E\u22a5,:B)/norm(:B)^2\nex=[1,0,0];ey=[0,1,0];ez=[0,0,1]\nB=:B\u2256:Bt*Vec(ez)\nBt=:Bt\u22561.5\nr=:r\u22561\ndBt=:dBt\u22560.3\nEperp=:E\u22a5\u2256-:r/2*:dBt*Vec(ey)\nvars=[B,Bt,Eperp,r,dBt]\nprintln(ve&vars)\nprintln(ve&Eperp&B)", "outputs": [{"output_type": "stream", "name": "stdout", "text": "ve \u2256 (-0.09999999999999999) Vec([1,0,0])\nve \u2256 (-0.5) dBt r \u2571(Bt) Vec([1,0,0])\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 13, "cell_type": "code", "source": "equ=Equation\n\n# Compression factor\nop1=equ(:rt,:r0*sqrt(:Bz0/:Bzt))\nop3=equ(:rt,:r0*:Bzt/:Bz0)\n\nBpz=equ(:B\u0307z,0.1)\nBz0=equ(:Bz0,5)\nr0=equ(:r0,3)\nrp=equ(:r\u0307,-0.5*:r/:Bz*:B\u0307z)\nrp0=equ(:r\u03070,-0.5*:r0/:Bz0*:B\u0307z)\nvars=[rp0,Bpz,Bz0,r0]\nrd=equ(:r\u0394,:r0+:r\u03070)\nBzd=equ(:Bz\u0394,:Bz0+:B\u0307z)\nBzds=Bzd&vars\nrds=rd&rp0&vars\nrdn=(op1&equ(:Bzt,:Bz\u0394)&vars&Bzds).rhs #n=numeric\n\nnsteps=9\nrq=rd\nrqn=rds.rhs\nop1s=rdn\nBqn=Bzds.rhs\nfor step in 1:nsteps #q=r-1\n\trqp=-0.5/Bqn*rq.rhs*:B\u0307z\n\trr=equ(symbol(\"r$(step)\u0394\"),rqn+rqp)\n\trrs=rr&vars\n\tprint(rrs,\" \\t\")\n\tBr=equ(symbol(\"Bz$(step)\u0394\"),Bqn+:B\u0307z)\n\tBrs=Br&vars\n\tprintln((op1&equ(:Bzt,symbol(\"Bz$(step)\u0394\"))&vars&Brs))\n\tBqn=Brs.rhs\n\trqn=rrs.rhs\nend\n", "outputs": [{"output_type": "stream", "name": "stdout", "text": "r1\u0394 \u2256 2.940882352941176 \trt \u2256 2.9417420270727606\nr2\u0394 \u2256 2.912324660633484 \trt \u2256 2.913857587071793\nr3\u0394 \u2256 2.8843057927089557 \trt \u2256 2.886751345948129\nr4\u0394 \u2256 2.856805792708956 \trt \u2256 2.8603877677367775\nr5\u0394 \u2256 2.8298057927089557 \trt \u2256 2.8347335475692046\nr6\u0394 \u2256 2.8032879355660985 \trt \u2256 2.8097574347450824\nr7\u0394 \u2256 2.777235303987151 \trt \u2256 2.785430072655779\nr8\u0394 \u2256 2.751631855711289 \trt \u2256 2.7617238536949706\nr9\u0394 \u2256 2.726462364185865 \trt \u2256 2.7386127875258315\n"}], "metadata": {"collapsed": false, "trusted": true}}, {"execution_count": 14, "cell_type": "code", "source": "# Temperatures\nEkin=equ(:Ekin,0.5*:Tpa+:Tpe)\nparfac=1\nTpa1=equ(:Tpa1,parfac*:T0) #is parallel temperature affected?\nTpe1=equ(:Tpe1,2*:T0)\nprintln(Tpa1,\", \",Tpe1)\nEk1=equ(:Ek1,0.5*:Tpa1+:Tpe1)\nEk2=equ(:Ek1,0.5*:T2+:T2)\nEk1s=Ek1&Tpa1&Tpe1 #s=solved\nT2=(Ek2&Ek1s)/1.5\nprintln(T2)\nTpa3=equ(:Tpa3,1/parfac*:T2) #is it?\nTpe3=equ(:Tpe3,:T2/2)\nEk3=equ(:Ek3,0.5*:Tpa3+:Tpe3)\nEkf=[equ(:Ekf,0.5*:Tf+:Tf),equ(:Ekf,:Ek3)]\nTf=(Ekf[1]&Ekf[2]&Ek3&Tpa3&Tpe3&T2)/1.5\nprintln(Tf) #nope\n", "outputs": [{"output_type": "stream", "name": "stdout", "text": "Tpa1 \u2256 1 T0, Tpe1 \u2256 2 T0\nT2 \u2256 1.6666666666666665 T0\nTf \u2256 1.111111111111111 T0\n"}], "metadata": {"collapsed": false, "trusted": true}}], "nbformat": 4, "metadata": {"kernelspec": {"display_name": "Julia 0.3.6", "name": "julia 0.3", "language": "julia"}, "language_info": {"version": "0.3.6", "name": "julia"}}}
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