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Plasma Parameters Widget

This is the permanent web page for the Plasma Parameters Widget. I previously made a new page for each iteration of the widget, but that seems unnecessary since there are so few changes between them.


Status and Download



This is a Dashboard widget that calculates an assortment of relevant plasma parameters given user inputs of basic characteristics. For example, the user provides the background magnetic field and the widget displays the electron cyclotron frequency. Most of the equations used to calculate these parameters are taken directly from the Naval Research Laboratory's (NRL) Plasma Formulary, a source that has been vetted by the plasma physics community over the past few decades. Some parameters, including the Bremsstrahlung radiated power, are taken from sources provided by plasma physicists since this widget was first made public.


How it Works

plasma parameters widget screenshot
Widget screenshot demonstrates the equation pop-up that appears when the cursor is held over a label. In this case the cursor is held over the text "fce".

This is a simple javascript-based calculator. You provide input values relating to the most basic properties of the plasma and then various length, frequency, and velocity parameters are output. The figure to the right is a screenshot of the widget illustrating the default display with a help window. The area above the “Calculate” and “Choose Preset...” buttons is for the input parameters. These input parameters and their required units are,

  • Bo: Magnetic Field [Gauss]
  • μ: Ion Mass Factor [unitless], the ratio of the ion species mass to the mass of a proton
  • Z: Charge Factor [unitless], atomic number of the ion species
  • γ: Adiabatic Index [unitless]
  • ne: Electron Density [cm-3]
  • Te: Electron Temperature [eV]
  • Ti: Ion Temperature [eV]
  • ln(Λ): Coulomb Logarithm [unitless], a collision parameter
  • R: (secondary display) Tokamak Major Radius [m]
  • a: (secondary display) Tokamak Minor Radius [m]

You are not required to provide a value for each input. All of the parameters that can be calculated from the values that have been provided will be displayed. Any other output will return “NaN” to signify “Not a Number”. Using one of the preset input sets will provide decent values that you might want to use as the value for inputs you do not know for certain.

The output parameters and their units are,

fce: Electron Cyclotron Frequency [Hz]
Electron Cyclotron Frequency
fci: Ion Cyclotron Frequency [Hz]
Ion Cyclotron Frequency
fpe: Electron Plasma Frequency [Hz]
Electron Plasma Frequency
fpi: Ion Plasma Frequency [Hz]
Ion Plasma Frequency
νe: Electron Collision Frequency [Hz]
Electron Collision Frequency
νi: Ion Collision Frequency [Hz]
Ion Collision Frequency
re: Electron Gyroradius [m]
Electron Gyroradius
ri: Ion Gyroradius [m]
Ion Gyroradius
vthe: Electron Thermal Velocity [m/s]
Electron Thermal Velocity
vthi: Ion Thermal Velocity [m/s]
Ion Thermal Velocity
δe: Plasma Skin Depth [m]
Plasma Skin Depth
Cs: Ion Sound Speed [m/s]
Ion Sound Speed
vA: Alfén Velocity [m/s]
Alfén Velocity
λD: Debye Length [m]
Debye Length
β: Beta [unitless]
ι: Ion Inertial Length [m]
Ion Plasma Frequency
ftr: Trapped Particle Fraction (Toroidal Geometry) [unitless]
Trapped Particle Fraction
Pbr: Bremsstrahlung Radiated Power [W/m3]
Bremsstrahlung Radiated Power
λe: Electron Mean Free Path [m]
Electron Mean Free Path
Prec: Recombination Radiated Power [W/m3]
Recombination Radiated Power
λi: Ion Mean Free Path [m]
Ion Mean Free Path
Pline: Line Radiated Power [W/m3]
Line Radiated Power

Placing the cursor over any of the parameters labels causes a help window to pop-up. This window displays the equation used to calculate the parameter. This is the example shown in the screenshot.



The information side (reached by clicking the “i” button in the lower right hand corner) allows you to set preferences. The checkbox labeled, “Show Tokamak Side as Default” determines which output parameters are visible by default. The screenshot shown previously displays the primary parameters. Holding the cursor over the infinity button at the bottom of the widget will cause this primary screen to disappear and the “Tokamak Side” to display. The tokamak pane includes the radii input and the mean free path and radiated power output parameters. Placing a check in the aforementioned box causes the tokamak (secondary) panel to display by default. If this is set, then placing the cursor over the infinity button causes the primary parameters to display.

The rollover help only works for the default display. If you have the primary parameters as the default, then you cannot place the cursor over the secondary parameters in order to view the help window. This will be obvious when you move the cursor away from the infinity button and witness the disappearance of the displayed parameters before being able to view their help windows.

Default values for the major and minor radius can be set in the appropriately labeled areas. These will appear in the input display automatically. Entering a number in the preference areas sets the default, there is no need to press .

The remaining input areas on the information side allow for you to create a preset. These will serve as the “My Set” collection provided by the drop down button on the front side. Typing values into the text areas on the information side will set them as the preference.



It is possible to alter the expression of any output parameter by modifying the javascript code used for the calculations. To view the relevant code, browse to Library\Widgets\plasmaParams4-1.wdgt in Finder. This is in the Library folder of your personal user account (not the system-wide Library). Control-click, or right click, the widget file and select “Show Package Contents”. A new Finder window will open and display all the files of the widget. The file with the equations for calculating the output parameters is named plasmaParams.js

Open this file with the text editor of your choice. Find the line (probably line 186) that reads,

function calcParams(event)

This is the function in which the parameters are calculated. Change it as you see fit, save it, and then try the widget anew. It is probably a good idea to copy the entire widget to a new directory and then attempt to change it. Also, you can always contact me to suggest changes and improvements.



The following acknowledgments section can be found on the information side of the widget.

This widget is primarily based on the Plasma Formulary published by the Naval Research Laboratory (NRL). The NRL provides hard copies of the Formulary for free, and I also thank them for that service.

Additionally, I would like to extend my gratitude to the following people for their help.

Joe Huba (NRL): for allowing me to include the official formulary link and suggesting that space plasmas receive better treatment in the output. He further suggested the inclusion of the ion inertial length, ι, and provided the expression for it.

Aaron Roberts (NASA): for providing Solar Wind parameters and suggesting better handling of space plasma parameters.

Melvyn Goldstein (NASA): for providing Solar Wind parameters and seconding the request for better handling of space plasma parameters. He also demonstrated the usefulness of including the adiabatic index as an input parameter.

Thomas Pedersen (Columbia University): for pointing out errors in some of the calculations.

Frank J. Wessel (University of California, Irvine): for suggesting the inclusion of radiation emission power and providing the necessary reference. The expressions for radiation power are taken from page 234 of “Fusion Plasma Analysis” by Weston M. Stacey, Jr. (© 1981, John Wiley and Sons, Inc., Reprinted with corrections in 1992).

UCLA Plasma Physics Group: Brian Brugman, Troy Carter, Neal Crocker and Anne White all helped with the initial development of this widget by troubleshooting and making suggestions for useful calculations.


Required Apple Statement

"Mac OS X 10.4 Tiger is required. If youre using Safari, click the download link. 
When the widget download is complete, show Dashboard, click the Plus sign to 
display the Widget Bar and click the widgets icon in the Widget Bar to open it. If 
youre using a browser other than Safari, click the download link. When the widget 
download is complete, unarchive it and place it in /Library/Widgets/ in your home 
folder. show Dashboard, click the Plus sign to display the Widget Bar and click the 
widgets icon in the Widget Bar to open it."

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Initial Posting: Wednesday, 09 July 2008
Last Updated: Friday, 09 December 2011