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))
    ax = fig.add_subplot(111)

    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=d, 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')