Collisions between charged particles.

How did the particles get there?

Lets us look at an astrophysical gasin equilibrium.

Since it is mostly H, take pure H.

H is composed of e- & p+ must come into equilibrium.

Ionization Equilibrium

Will they stick together of merely pass by?

Will the H split up or not?

Energy in building compared to energy in thermal velocity.

Heat to T, let enough time pass so all particles collide.

Then how many atoms N+ are ionized compared to how many No are neutral.

Given by Sara’s equation:

Where does this come from?

From Boltymann Equation

based on quantum mechanical definition of temperature – must be ttrue by definition

Very general application

What energy states are available in our simple 2 state system?

0 (unionized)


gB(v,T) quantum mechanical function\

Saha Equation rue only in thermal equilibrium.

Thrue if collisions up and down determine balance

Interstellar gas is very thin. What if radiation dominates recombination?

Saha equation is then inapplicable—

Boltzmann does not hold

Microprocesses Dominate

Einstein coefficients domintae collision rate.

Take Lya – 10-4 sec to recombine


v = 1.6 * 106 cm s-1

In 10-4 s, moves 160 cm

If no collisions, then Saha does not hold

In this room, n ~ 1021 cm-3



Ready for Bremsstrahlung

Take pure H at T >> 104 K (totally ionized)

Basic collisions: ep, ee, pp (ee and pp have no dipole compontent, weak emitters)

Electron-proton interactions dominate

put these together and assume

imagine uniform beam then

Ebdb = E * 2p b db


frequency distribution




total power

erg cm-3 c-1


density of electrons collision E emitted by collision at V

at v fequency averaged over b

density of ions




need f(v)d3v and En(n)

First, En(n)

Emits at n if t ~1/w = 1/(2pn)

sum all radiation at n from all b’s











Take a ball of gas volume = V

Pure H => ne = np

Temp = T


E=nV 3/2 kT

t = E/P =


Flare – measure t –watch intensity

Measure T --watch spectrum


Line Emission

Put heavy elements back in

X ~ Z2

Heavy elements can be partially ionized in a gas.

FeI, FeII … FeXVII at 107K

After heavy elements stripped then pure bremsstrahlung holds as derived. But at intermediate T line emission can dominate

When an electron collies with an ion the ound electronscan get bumped into a higher state. Will then radiatively decay. This is efficient because electrons have just the right amount of energy to excite the ions.

Line Emission dominates: at some T, pure bremsstrahlung <1% of emission

Thus the small impurities dominate





Compton Scattering

In this frame both particles merely reverse direction

But this is not the case in the general fram of reference

Electron has

Photon has







In a plasma repeated Compton scattering will blur features by 0.024 per scatter. Comptonize spectrum is smooth.

Inverse Compton Effect

Take relativistic electrons and send a beam of photons through

If g = 104

n =108ni

take an optical photon 5000

after scatter 5*10-5 = 2*108 eV

Even microwave background

T = 3 T = 3*108K (x-rays)

Power distribution of electrons Power law spectrum