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Lecture 3-Bremsstrahlung (free-free) (General (Produced by any ionised gas…
Lecture 3-Bremsstrahlung (free-free)
General
Produced by any ionised gas, mostly hydrogen
caused by the coulomb interactions between oppositly charged particles in an ionised gas
Ionise a gas with photons to overcome binding energy
Diagram
In a hot gas particles will move with velocities proportional to the temperature of the gas
H2 regions have temp 3000-10000K
Hydrogen
Mst abundant element in universe
neutral exits mainly in cold clouds and early universe. Electron bound to proton
ionised will have equal no. of protons and electron, unbound (free-free)
How specifics
Proton and electron produce electric fields
fields are equal in strength and opposite in sign
exert a force because of fields
different mass means different effect
causes electron to accelerate towards the proton
Coulomb interaction maths
Proton emits a spherically symmetric electric field
At the position of the electron, the strength of the electric field can be resolved into the x and z directions
use lorentz force and newtons 2nd law
switch between acceleration as a function of time and acceleration as a function of angular frequency using their fourirer relationship
no dependance on omega
Frequency spectrum of the emission from a single electron proton interaction is simply flat
makes sense since electron experiences an impulse of energy in time. FT of impulse is a flat line
Multiple encounters and averaging over velocity
The number of protons an electron moving with speed v will encounter within a range of impact parameters during time interval is equivalent to integral over a cylindrical shell
Maxwellian distribution of velocities
Gaunt factor
Lots of maths