(153)
where the terminal velocity V_infinity is given by equation (104) and the local speed of sound a by equation (106). Substitution into equation (153) yields:
(154) 
The parallel component of the terminal thermal velocity V_parallel,_infinity,_thermal in the reference frame of the beam in terms of T_parallel,_infinity as discussed earlier and is given by:
(155) 
Solving for T_parallel,_infinity and substituting into equation (154) yields:
(156) 
Since the terminal Mach number is a parameter frequently used for characterizing the width of the velocity distribution, we can see that the larger the terminal Mach number the more narrow the velocity distribution, for a given T_o and gas.
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