(* This notebook is my attempt to calculate the required magnetic field gradient that the Zeeman Slower should have. My lack of quantum mechanics is showing *)


(3 1.381 (600+273) 6.022/0.08762)^(1/2)

Solve[r == -(v-vo)^2/(2 A)-vo(v-vo)/A,v]

J = kg m^2/s^2;
ns = 10^-9s;
nm = 10^-9 m;
MHz = 10^6 s^-1;

h = 6.626 10^-34 J s;
c = 3 10^8 m/s;
gamma = 15ns;
M = 0.08762kg/(6.022 10^23);
Ft = c/(460 nm);
ΔFl = -500 MHz;
Vo = 500 m/s;
sigma = 1;

a = -h Ft/(gamma M c);
V = (Vo^2 + 2 a z m)^(1/2);
Solve[V==0 m/s,z]

B = Simplify[s/sigma(ΔFl + (Ft + ΔFl)((c+V)/(c-V))^(1/2)),{kg>0,s>0,m>0}]

Plot[Log[10,B],{z,0,0.3},PlotRange->Full]

Plot[Simplify[((c+V)/(c-V))^(1/2)-1,{kg>0 ,s>0,m>0}],{z,0,0.18939572407962238},PlotRange->Full,AxesLabel->{z,"doppler shift - 1"}]

Plot[Simplify[s/m V,{s>0,kg>0,m>0}],{z,0,0.18939572407962238},PlotRange->Full]