Question

A distant galaxy consists from a cloud of protons and antiprotons with the same density n = 106 m^(-3) and a temperature of 100 K. What is the Debye radius?

Answer 1

Debye radius is a characteristic distance over which the screening of the Coulomb field in the plasma is performed and from which the plasma is electrically neutral. Since the density of protons and antiprotons is the same, we consider that the plasma is quasi-neutral.

Proton charge is (-e), antiproton charge is e, Tp=Tap, Np=Nap:
rD = ie*i2*Ni*ϵ0*k*Ti - 1 = e*p2*Np*ϵ0*k*Tp+ ea*p2*Nap*ϵ0*k*Tap - 1 = ϵ0*k*Tp*2ep*2Np = k*Tp*2*4πep*2Np = 691002*106 = 0.6912 = 0.49 m