# File:Paschen curves.svg

Original file(SVG file, nominally 575 × 571 pixels, file size: 63 KB)

## Summary

Description
English: Paschen curves obtained for Helium, Neon, Argon, Hydrogen and Nitrogen, using the expression for the breakdown voltage as a function of the parameters A, B that interpolate the first Townsend coefficient.

$V_{B}={\frac {B\cdot pd}{\ln(A\cdot pd)-\ln \left[\ln \left(1+1/\gamma _{sc}\right)\right]}}$ The source for parameter values for A and B is provided in the code.
Date
Source Own work
Author Krishnavedala
SVG development

## Python

Source code
import matplotlib.pyplot as plt
import numpy as np

def paschen(a, b, pd):
# using gamma = 0.01
V = b * pd / (np.log((a * pd) / np.log(1+1/.01)))
return pd[V > 10], V[V > 10]

if __name__ == "__main__":

fig = plt.figure(figsize=(7,7))

pd = np.logspace(-1,3, 500)

''' coefficients for He, Ne, Ar, H2, N2 from Table 14.1 on Page: 546 of:
Lieberman, M. A., & Lichtenberg, A. J. (2005). Principles of plasma discharges
and materials processing. Hoboken, N.J: Wiley-Interscience. 2nd Edition
'''
data = {
r'He':    {'A':  2.8, 'B':  77},
r'Ne':    {'A':  4.4, 'B': 111},
r'Ar':    {'A': 11.5, 'B': 176},
r'H$_2$': {'A':  4.8, 'B': 136},
r'N$_2$': {'A': 11.8, 'B': 325},
}

for d in data:
p, V = paschen(data[d]['A'], data[d]['B'], pd)
ax.plot(p, V, label=E[i], linewidth="2")

ax.set_xscale("log", nonposx='clip')
ax.set_yscale("log", nonposy='clip')
ax.set_xlim(1e-1, 1e3)
ax.set_ylim(1e2,1e6)
ax.set_xlabel(r'$pd$ [Torr cm]')
ax.set_ylabel(r'$V_B$ (Volt)')
ax.grid(True)
plt.minorticks_on()
plt.legend(loc=0, frameon=False, numpoints=2)
fig.savefig('Paschen curve.svg', \
bbox_inches='tight', \
transparent='true')


## Licensing

I, the copyright holder of this work, hereby publish it under the following license:   This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license. You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

## File history

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Date/TimeThumbnailDimensionsUserComment
current15:31, 8 September 2014 575 × 571 (63 KB)KrishnavedalaUser created page with UploadWizard
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## Global file usage

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• Usage on ar.wikipedia.org
• Usage on hi.wikipedia.org