To the Quantum Limitations in Beam Physics

number of states equals to the number of the particles in the beam. This definition basically corresponds to assumption that the beam has zero temperature. We will simply calculate the number of allowed states. The second approach, indeed, uses the definition of the beam temperature in a moving system of reference. We compare the emittance restrictions obtained with these two approaches. Ultrarelativistic electron gas becomes more ideal in a Lab frame with increasing its energy due to cancellation of forces between the particles as ≈1 2 /γ . In principle, some amount of particles with opposite charge can be added to the beam moving along a straight line in a focusing channel [7]. Now let us estimate the minimal emittance from the compact packing approach. For the electrons in a volume V, the number of states with absolute magnitude of momentum in the interval from px y s , , to p dp x y s x y s , , , , + is