# 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.

${\displaystyle V_{B}={\frac {B\cdot pd}{\ln(A\cdot pd)-\ln \left[\ln \left(1+1/\gamma _{sc}\right)\right]}}}$

The source for parameter values for A and B is provided in the code.
Date
Source Own work
Author Krishnavedala
SVG development
 This plot was created with Matplotlib.

## 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:

## File history

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Date/TimeThumbnailDimensionsUserComment
current15:31, 8 September 2014575 × 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