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    Building, troubleshooting and testing of these amplifiers should only be
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Low voltage high current rectification

There are formulas in the catalog to calculate effect of DC current on permeability coupled with mu-H curves. According to this information, the T106-45 60-turn inductor will have approximately half of its no-DC inductance at 4A DC, or about 220 mH. However, high AC magnetization will somewhat compensate for the loss of permeability, so it will be in the ballpark of 300-350 mH. Same is true for the MP inductor, for whose material permeability drops faster with DC magnetization, but it has longer magnetic path and fewer turns.
The stored energy of a 220mH inductor at 4Amps is Eind =0.5 * L * I² = 0.5 * 0.22 * 16 = ca 1.7J .
Fantastic!
About 1000 times bigger than the real cores I do know.
Please give a link to that calculation
 
Micrometals iron powder catalog page 34:

Micrometals catalog

Graph in the right hand corner of the page gives the formula H=0.4 x pi x N x I / Le, where
H - magnetizing force, Oe;
N - number of turns, in this case 60.
I - DC current, A, 4.
Le - magnetic path length, cm, 6

With these numbers, H is approximately 48 Oe. On the graph find mu at this H, about 45% of initial. Multiply zero DC inductance of 440 uH by 0.45, get 198 uH.
 
So I took the formula of your link into a spreadsheet and this is what I calculate for 1, 50 and 60 turns.
As expected, the stored energy is independent of number of turns and with <2.5mJ well within expected range.
 

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This is not a smoothing choke. The purpose of the first choke in a choke input filter is to provide uninterrupted sinusoidal current in power transformer secondary and improve output voltage regulation. For this purpose the first choke must have at least the minimum inductance value, aka critical inductance. For 2.5 V 4 A, the critical value is about 0.4 - 0.5 mH. The impedance of the first choke at specific frequencies doesn't matter (if we disregard frequency-dependent change of inductance). Filtering should be regarded in conjunction with downstream elements, capacitors and smoothing chokes.
 
I could do it in PSUD2, but it doesn't have a choice for a pair of 10 A Ge diodes with CT transformer secondary. It would be easier to assemble the circuit and measure. It won't show transients though. Diodes will definitely need voltage and current protection, which I will discuss in a separate post.
 
Other options for input choke are air core and standard gapped iron EI core. Here are Fosgate 5.1 mH air core choke and small 0.8 mH 6A EI choke. Air core is wound with 14 AWG wire and weighs half-pound, but inductance is independent of DC current.
 

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Ge rectifier derating

Current rating of Ge rectifiers is at case temperature of 20 degrees C. From D305 data sheet, at 55 C case temperature, the maximum allowable current is 60% of the rated, or 6A. Dissipated power at 6A is 0.35 V x 3A = 1 W, so diodes must be on heat sinks. Case temperature should not exceed 60 C, otherwise there could be thermal runaway.