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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "5b8f9968",
+   "metadata": {},
+   "source": [
+    "# PlasmaPy Tutorial"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c8c364e5",
+   "metadata": {},
+   "source": [
+    "[`astropy.units`]: https://docs.astropy.org/en/stable/units/index.html\n",
+    "[`plasmapy.particles`]: https://docs.plasmapy.org/en/stable/particles/index.html\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "[`plasmapy.dispersion`]: https://docs.plasmapy.org/en/stable/dispersion/index.html\n",
+    "\n",
+    "Thank you for coming to this interactive tutorial. 🌱 We are excited for you to be here! 😺\n",
+    "\n",
+    "PlasmaPy is an open source Python package for plasma research and education. We will go through some interactive examples of using [`plasmapy.particles`] ⚛ and [`plasmapy.formulary`] 🧮.\n",
+    "\n",
+    "Let's start with some preliminary imports & settings. To execute a cell in a Jupyter notebook, press `Shift + Enter`. If you have to restart the notebook, please re-execute the following cell.\n",
+    "\n",
+    "If using Google Colab, click **Run anyway** when prompted. (If prompted again, select **Restart runtime** when the installation finishes.)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fa326226",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import sys\n",
+    "\n",
+    "if 'google.colab' in str(get_ipython()):\n",
+    "    if 'plasmapy' not in sys.modules:\n",
+    "        !pip install plasmapy==2024.5.0\n",
+    "\n",
+    "import numpy as np\n",
+    "import astropy.units as u\n",
+    "from astropy import constants as const\n",
+    "from plasmapy.particles import *\n",
+    "from plasmapy.formulary import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6e8f0d92",
+   "metadata": {},
+   "source": [
+    "## Quick refresher on `astropy.units`"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "93658d4f",
+   "metadata": {},
+   "source": [
+    "[`astropy.units`]: https://docs.astropy.org/en/stable/units/index.html\n",
+    "\n",
+    "PlasmaPy makes heavy use of [`astropy.units`], which is my favorite part of the scientific pythoniverse!  We typically import this subpackage as `u`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8c20320a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import astropy.units as u"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9ccbb06",
+   "metadata": {},
+   "source": [
+    "We can create a physical quantity by multiplying or dividing a number or array with a unit."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8437650a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "60 * u.km"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ccc6659f",
+   "metadata": {},
+   "source": [
+    "[`Quantity`]: https://docs.astropy.org/en/stable/api/astropy.units.Quantity.html#astropy.units.Quantity\n",
+    "\n",
+    "This operation creates a [`Quantity`] object: a number, sequence, or array that has been assigned a physical unit.  We can create [`Quantity`] objects with compound units."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "4932159b",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/latex": [
+       "$88 \\; \\mathrm{\\frac{mi}{h}}$"
+      ],
+      "text/plain": [
+       "<Quantity 88. mi / h>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "88 * u.imperial.mile / u.hour"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "97a8d49a",
+   "metadata": {},
+   "source": [
+    "## Particles"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0c7eeced",
+   "metadata": {},
+   "source": [
+    "[`plasmapy.particles`]: https://docs.plasmapy.org/en/stable/particles/index.html\n",
+    "\n",
+    "The [`plasmapy.particles`] subpackage contains functions to access basic particle data and classes to represent particles."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "24125310",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from plasmapy.particles import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e224284a",
+   "metadata": {},
+   "source": [
+    "### Particle properties"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7696deba",
+   "metadata": {},
+   "source": [
+    "[representation of a particle]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.ParticleLike.html#particlelike\n",
+    "\n",
+    "There are several functions that provide information about different particles that might be present in a plasma. The input of these functions is a [representation of a particle], such as a string for the atomic symbol or the element name."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "006b8d3e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "atomic_number(\"Fe\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2aa5af34",
+   "metadata": {},
+   "source": [
+    "[atomic number]: https://en.wikipedia.org/wiki/Atomic_number\n",
+    "\n",
+    "We can provide a number that represents the [atomic number]."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "69958326",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "element_name(26)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cca89cef",
+   "metadata": {},
+   "source": [
+    "We can provide standard symbols or the names of particles."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "16ca5b6f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "is_stable(\"e-\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "35d8e49e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "charge_number(\"proton\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8f2e5b30",
+   "metadata": {},
+   "source": [
+    "[mass number]: https://en.wikipedia.org/wiki/Mass_number\n",
+    "[`Quantity`]: https://docs.astropy.org/en/stable/units/quantity.html#quantity\n",
+    "[`astropy.units`]: https://docs.astropy.org/en/stable/units/index.html\n",
+    "[`half_life`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.atomic.half_life.html#half-life\n",
+    "\n",
+    "We can represent isotopes with the atomic symbol followed by a hyphen and the [mass number]. Let's use [`half_life`] to return the half-life of a radioactive particle in seconds as a [`Quantity`]."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "94fcf452",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "half_life(\"C-14\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "58ab7782",
+   "metadata": {},
+   "source": [
+    "We typically represent an ion in a string by putting together the atomic symbol or isotope symbol, a space, the charge number, and the sign of the charge."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a65e15da",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "charge_number(\"Fe-56 13+\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ce4886cf",
+   "metadata": {},
+   "source": [
+    "[particle-like]: https://docs.plasmapy.org/en/latest/glossary.html#term-particle-like\n",
+    "[`plasmapy.particles`]: https://docs.plasmapy.org/en/stable/particles/index.html\n",
+    "\n",
+    "Functions in [`plasmapy.particles`] are quite flexible in terms of string inputs representing particles. An input is [particle-like] if it can be used to represent a physical particle.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "05e03a8b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_mass(\"iron-56 +13\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "0dd9541b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_mass(\"iron-56+++++++++++++\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d3adf3a6",
+   "metadata": {},
+   "source": [
+    "Most of these functions take additional arguments, with `Z` representing the charge number of an ion and `mass_numb` representing the mass number of an isotope. These arguments are often [keyword-only](https://docs.plasmapy.org/en/latest/glossary.html#term-keyword-only) to avoid ambiguity."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "61e0f960",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "particle_mass(\"Fe\", Z=13, mass_numb=56)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "53a1d993",
+   "metadata": {},
+   "source": [
+    "### Particle objects"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3c2c3835",
+   "metadata": {},
+   "source": [
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle\n",
+    "\n",
+    "Up until now, we have been using functions that accept representations of particles and then return particle properties. With the [`Particle`] class, we can create objects that represent physical particles."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "fe9f824a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "proton = Particle(\"p+\")\n",
+    "electron = Particle(\"electron\")\n",
+    "iron56_nuclide = Particle(\"Fe\", Z=26, mass_numb=56)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "160df55b",
+   "metadata": {},
+   "source": [
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle\n",
+    "\n",
+    "Particle properties can be accessed via attributes of the [`Particle`] class."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bebcc477",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "proton.mass"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "df0f2eed",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "electron.charge"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "116cd6ad",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "electron.charge_number"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "99d22bd3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron56_nuclide.binding_energy"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8986cef8",
+   "metadata": {},
+   "source": [
+    "#### Antiparticles\n",
+    "\n",
+    "[`antiparticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle.antiparticle\n",
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle\n",
+    "\n",
+    "We can get antiparticles of fundamental particles by using the [`antiparticle`] attribute of a [`Particle`]."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "f6663952",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "electron.antiparticle"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bf40e592",
+   "metadata": {},
+   "source": [
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle\n",
+    "\n",
+    "\n",
+    "We can also use the tilde (`~`) operator on a [`Particle`] to get its antiparticle."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "180a1edf",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "~proton"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8500bc48",
+   "metadata": {},
+   "source": [
+    "#### Ionization and recombination\n",
+    "\n",
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle\n",
+    "[`recombine()`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle.recombine\n",
+    "[`ionize()`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html#plasmapy.particles.particle_class.Particle.ionize\n",
+    "\n",
+    "The [`recombine()`] and [`ionize()`] methods of a [`Particle`] representing an ion or neutral atom will return a different [`Particle`] with fewer or more electrons."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "186b1dfa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "deuterium = Particle(\"D 0+\")\n",
+    "deuterium.ionize()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4ee95241",
+   "metadata": {},
+   "source": [
+    "When provided with a number, these methods tell how many bound electrons to add or remove."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "242b53bd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "alpha = Particle(\"alpha\")\n",
+    "alpha.recombine(2)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e5302bef",
+   "metadata": {},
+   "source": [
+    "### Custom particles"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4c8c2a63",
+   "metadata": {},
+   "source": [
+    "[`CustomParticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.CustomParticle.html\n",
+    "\n",
+    "Sometimes we want to use a particle with custom properties.  For example, we might want to represent an average ion in a multi-species plasma or a dust particle.  For that we can use [`CustomParticle`]."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "35b94505",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cp = CustomParticle(9e-26 * u.kg, 2.18e-18 * u.C, symbol=\"Fe 13.6+\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dfc19404",
+   "metadata": {},
+   "source": [
+    "[`CustomParticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.CustomParticle.html\n",
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html\n",
+    "\n",
+    "Many of the attributes of [`CustomParticle`] are the same as in [`Particle`]."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "8a4b412b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cp.mass"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a2da2b3b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cp.charge"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "ecb450f6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "cp.symbol"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "21a992a9",
+   "metadata": {},
+   "source": [
+    "[`numpy.nan`]: https://numpy.org/doc/stable/reference/constants.html#numpy.nan\n",
+    "\n",
+    "If we do not include one of the physical quantities, it gets set to [`numpy.nan`] (not a number) in the appropriate units."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a31c421a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "CustomParticle(9.27e-26 * u.kg).charge"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6292a1f3",
+   "metadata": {},
+   "source": [
+    "[`CustomParticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.CustomParticle.html\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "\n",
+    "[`CustomParticle`] objects can provided to most of the commonly used functions in [`plasmapy.formulary`], and we're planning to improve interoperability in future releases of PlasmaPy."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0f2b0634",
+   "metadata": {},
+   "source": [
+    "### Particle lists"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7939cfad",
+   "metadata": {},
+   "source": [
+    "[`ParticleList`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_collections.ParticleList.html\n",
+    "[`CustomParticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.CustomParticle.html\n",
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html\n",
+    "\n",
+    "The [`ParticleList`] class is a container for [`Particle`] and [`CustomParticle`] objects."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "30cc7d36",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron_ions = ParticleList([\"Fe 12+\", \"Fe 13+\", \"Fe 14+\"])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d56ddb98",
+   "metadata": {},
+   "source": [
+    "[`ParticleList`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_collections.ParticleList.html\n",
+    "\n",
+    "By using a [`ParticleList`], we can access the properties of multiple particles at once."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2434f71b",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron_ions.mass"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "14a431dd",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron_ions.charge"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "48cd1c7a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron_ions.symbols"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cccc6c60",
+   "metadata": {},
+   "source": [
+    "[`ParticleList`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_collections.ParticleList.html\n",
+    "[`CustomParticle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.CustomParticle.html\n",
+    "[`Particle`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_class.Particle.html\n",
+    "\n",
+    "We can also create a [`ParticleList`] by adding [`Particle`] and/or [`CustomParticle`] objects together."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3b953065",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "proton + electron"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "b78ee7d2",
+   "metadata": {},
+   "source": [
+    "We can also get an average particle."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "bf01f619",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "iron_ions.average_particle()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e9038618",
+   "metadata": {},
+   "source": [
+    "[`ParticleList`]: https://docs.plasmapy.org/en/stable/api/plasmapy.particles.particle_collections.ParticleList.html\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "\n",
+    "[`ParticleList`] objects can also be provided to the most commonly used functions in [`plasmapy.formulary`], with more complete interoperability expected in the future."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "efe199c8",
+   "metadata": {},
+   "source": [
+    "### Nuclear reactions"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "58fb006b",
+   "metadata": {},
+   "source": [
+    "[`plasmapy.particles`]: https://docs.plasmapy.org/en/stable/particles/index.html\n",
+    "\n",
+    "We can use [`plasmapy.particles`] to calculate the energy of a nuclear reaction using the `>` operator.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d8a9ab9e",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "deuteron = Particle(\"D+\")\n",
+    "triton = Particle(\"T+\")\n",
+    "alpha = Particle(\"α\")\n",
+    "neutron = Particle(\"n\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "cb95c644",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "energy = deuteron + triton > alpha + neutron"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "e7a4c236",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "energy.to(\"MeV\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8bf7e515",
+   "metadata": {},
+   "source": [
+    "If the nuclear reaction is invalid, then an exception is raised that states the reason why."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "67b32a3a",
+   "metadata": {
+    "tags": [
+     "raises-exception"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "deuteron + triton > alpha + 3 * neutron"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f065a288",
+   "metadata": {},
+   "source": [
+    "## PlasmaPy formulary\n",
+    "\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "\n",
+    "The [`plasmapy.formulary`] subpackage contains a broad variety of formulas needed by plasma scientists across disciplines, in particular to calculate plasma parameters."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "20c3b9b1",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from plasmapy.formulary import *"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "955ce3dd",
+   "metadata": {},
+   "source": [
+    "### Plasma beta in the solar corona"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1bb15c25",
+   "metadata": {},
+   "source": [
+    "[Plasma beta]: https://en.wikipedia.org/wiki/Beta_(plasma_physics)\n",
+    "\n",
+    "[Plasma beta] ($β$) is one of the most fundamental plasma parameters. $β$ is the ratio of the plasma (gas) pressure to the magnetic pressure. How a plasma behaves depends strongly on $β$. When $β ≫ 1$, the magnetic field is not strong enough to exert much of a force on the plasma, so its motions start to resemble a gas. When $β ≪ 1$, magnetic tension and pressure are the dominant macroscopic forces. \n",
+    "\n",
+    "Let's use [`plasmapy.formulary`](https://docs.plasmapy.org/en/stable/formulary/index.html) to calculate plasma β in different regions of the solar atmosphere and see what we can learn."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24162ca9",
+   "metadata": {},
+   "source": [
+    "#### Solar corona"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "60aa77b5",
+   "metadata": {},
+   "source": [
+    "Let's start by defining some plasma parameters for an active region in the solar corona."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c4b98f58",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "B_corona = 50 * u.G\n",
+    "n_corona = 1e9 * u.cm ** -3\n",
+    "T_corona = 1 * u.MK"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "cdc0c334",
+   "metadata": {},
+   "source": [
+    "When we use these parameters in [`beta`](https://docs.plasmapy.org/en/stable/api/plasmapy.formulary.dimensionless.beta.html#plasmapy.formulary.dimensionless.beta), we find that $β$ is quite small so that the corona is magnetically dominated."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "98b23229",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "beta(T=T_corona, n=n_corona, B=B_corona)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "deb41bfa-bad5-4bdc-a0f2-75b4c0a16054",
+   "metadata": {},
+   "source": [
+    "#### Solar photosphere"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2442b569-a98d-4528-ab1a-374867be06f3",
+   "metadata": {},
+   "source": [
+    "Let's specify some characteristic plasma parameters for the solar photosphere, away from any sunspots."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1654acbb-056b-46e5-9fcf-900ab0fbd2b7",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "T_photosphere = 5800 * u.K\n",
+    "B_photosphere = 400 * u.G\n",
+    "n_photosphere = 1e17 * u.cm ** -3"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "be434e24-080a-449e-a3f2-6f18149ff362",
+   "metadata": {},
+   "source": [
+    "When we calculate for the photosphere, we find that it is an order of magnitude larger than 1, so plasma pressure forces are more important than magnetic tension and pressure."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "7cf5b298-f68b-4bcb-bbf4-2fb93d8cdc6a",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "beta(T_photosphere, n_photosphere, B_photosphere)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dee08605",
+   "metadata": {},
+   "source": [
+    "### Plasma parameters in Earth's magnetosphere"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9587734f",
+   "metadata": {},
+   "source": [
+    "[magnetic reconnection]: https://en.wikipedia.org/wiki/Magnetic_reconnection\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "\n",
+    "The [*Magnetospheric Multiscale Mission*](https://www.nasa.gov/mission_pages/mms/overview/index.html) (*MMS*) is a constellation of four identical spacecraft. The goal of *MMS* is to investigate the small-scale physics of [magnetic reconnection] in Earth's magnetosphere. In order to do this, the spacecraft need to orbit in a tight configuration.  But how tight does the tetrahedron have to be?  Let's use [`plasmapy.formulary`] to find out."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "706818eb",
+   "metadata": {},
+   "source": [
+    "#### Physics background"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e7f1ddf9",
+   "metadata": {},
+   "source": [
+    "[Magnetic reconnection]: https://en.wikipedia.org/wiki/Magnetic_reconnection\n",
+    "\n",
+    "[Magnetic reconnection] is the fundamental plasma process that converts stored magnetic energy into kinetic energy, thermal energy, and particle acceleration. Reconnection powers solar flares and is a key component of geomagnetic storms in Earth's magnetosphere. Reconnection can also degrade confinement in fusion devices such as tokamaks.\n",
+    "\n",
+    "The **inertial length** is the characteristic length scale for a particle to get accelerated or decelerated by electromagnetic forces in a plasma.\n",
+    "\n",
+    "When the reconnection layer thickness is shorter than the **ion inertial length**, $d_i ≡ c/ω_{pi}$, collisionless effects and the Hall effect enable reconnection to be fast (Zweibel & Yamada 2009). The inner electron diffusion region has a thickness of about the **electron inertial length**, $d_e ≡ c/ω_{pi}$. (Here, $ω_{pi}$ and $ω_{pe}$ are the ion and electron plasma frequencies.)\n",
+    "\n",
+    "**Our goal: calculate $d_i$ and $d_e$ to get an idea of how far the MMS spacecraft should be separated from each other to investigate reconnection.**"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "749fba51",
+   "metadata": {},
+   "source": [
+    "### Length scales"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "9db83228",
+   "metadata": {},
+   "source": [
+    "Let's choose some characteristic plasma parameters for the magnetosphere."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "1f317f40",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "n = 1 * u.cm ** -3\n",
+    "B = 5 * u.nT\n",
+    "T = 10 ** 4.5 * u.K"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "591bef20",
+   "metadata": {},
+   "source": [
+    "Let's calculate the ion inertial length, $d_i$. On length scales shorter than $d_i$, the Hall effect becomes important as the ions and electrons decouple from each other."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a717c75f",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "inertial_length(n=n, particle=\"p+\").to(\"km\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5c56977f",
+   "metadata": {},
+   "source": [
+    "The ion diffusion regions should therefore be a few hundred kilometers thick. Let's calculate the electron inertial length next."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4e5a4dd9",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "inertial_length(n=n, particle=\"e-\").to(\"km\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "bb4b8d8d",
+   "metadata": {},
+   "source": [
+    "The electron diffusion region should therefore have a characteristic length scale of a few kilometers, which is significantly smaller than the ion diffusion region."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2b2875fc",
+   "metadata": {},
+   "source": [
+    "We can also calculate the gyroradii for different particles "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "96fee1ef",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "gyroradius(B=B, particle=[\"e-\", \"p+\"], T=T).to(\"km\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "1b2b32b3",
+   "metadata": {},
+   "source": [
+    "The four *MMS* spacecraft have separations of ten to hundreds of kilometers, and thus are well-positioned to investigate Hall physics during reconnection in the magnetosphere."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "38e1aff3",
+   "metadata": {},
+   "source": [
+    "#### Frequencies"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "fc1a183f",
+   "metadata": {},
+   "source": [
+    "We can also calculate some of the fundamental frequencies associated with magnetospheric plasma. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "4b9f9403",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "plasma_frequency(n=n, particle=[\"p+\", \"e-\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "5cc9c0ca",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "gyrofrequency(B=B, particle=[\"p+\", \"e-\"])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "88534868",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "lower_hybrid_frequency(B=B, n_i=n, ion=\"p+\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8242486e-dcb4-4815-aa6f-04e6d6406546",
+   "metadata": {},
+   "source": [
+    "[`lower_hybrid_frequency`]: https://docs.plasmapy.org/en/stable/api/plasmapy.formulary.frequencies.lower_hybrid_frequency.html#lower-hybrid-frequency\n",
+    "[`plasmapy.formulary`]: https://docs.plasmapy.org/en/stable/formulary/index.html\n",
+    "\n",
+    "\n",
+    "Most of the functions in [`plasmapy.formulary`] have descriptions of the plasma parameters that include the formula and physical interpretation.  If we ever forget what the [`lower_hybrid_frequency`] represents, we can check out its documentation page!  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "04bf2ba1-c580-4ca5-b410-530ad3b4e31a",
+   "metadata": {},
+   "source": [
+    "## Final thoughts"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "35962f6d-4897-4195-940d-990f36c313b3",
+   "metadata": {},
+   "source": [
+    "[PlasmaPy's online documentation]: https://docs.plasmapy.org\n",
+    "[contributor guide]: https://docs.plasmapy.org/en/latest/contributing\n",
+    "[getting ready to contribute]: https://docs.plasmapy.org/en/latest/contributing/getting_ready.html\n",
+    "[code contribution workflow]: https://docs.plasmapy.org/en/latest/contributing/workflow.html\n",
+    "[good first issues]: https://github.com/PlasmaPy/PlasmaPy/issues?q=is%3Aissue+is%3Aopen+label%3A%22good+first+issue%22\n",
+    "[raise an issue]: https://github.com/PlasmaPy/PlasmaPy/issues/new/choose \n",
+    "\n",
+    "Thank you for coming to this tutorial!  If you'd like to learn more about PlasmaPy's current capabilities, please check out [PlasmaPy's online documentation].\n",
+    "\n",
+    "PlasmaPy is a community-developed project, and we invite you to contribute!  Please check out our [contributor guide] to learn more, including the pages on [getting ready to contribute] and the [code contribution workflow].  We've labeled [good first issues] for new contributors.  Possibilities include improving the documentation for a plasma parameter or adding a new example Jupyter notebook.  \n",
+    "\n",
+    "If there is a feature that you would really like added to PlasmaPy, or if you find a bug or a place that the docs could be improved, please [raise an issue]!  We deeply appreciate it, and doing so helps guide the future of the project.\n",
+    "\n",
+    "We thank you once again!"
+   ]
+  }
+ ],
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