I finished reading all of the textbooks in my reading list, and none of them described the particle physics theory for deflection... except Zworykin, who walked step by step through the derivation in chapter 14 of the second edition of his textbook "Television". From first principles, he describes the derivation of the formulas that link the circuit theory of current through an inductor generating a magnetic field to the amount of magnetic energy needed to deflect a cathode ray by alpha degrees:
K = ratio of deflection core diameter to inner deflection diameter (typical value is around 1.66)
D = CRT neck diameter
V = CRT acceleration anode voltage
alpha = peak deflection angle required after recycled damper current is exhausted
W = the magnetic energy in joules.
This can then be combined with the standard formula for the magnetic energy
(L*I^2)/2 generated by current
I in amps through an inductance
L in henries, to calculate the peak current and average current needed to sweep a screen. I have created an automated calculator for these formulas in a Google spreadsheet
here. Just copy the spreadsheet and update the input parameter values to see the output amplifier design requirements for a given CRT, yoke, and output transformer. Below is a screenshot of what the calculator looks like, with example values for the CRT and yoke that I am using in my DIY TV:
