Electrical Generators; Excitation/Self induction start up

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Smaller electrical generators can be self-excited, using remnant magnetism to initiate a magnetic field that generates current in the armature. This process, known as "bootstrap," allows the generator to increase its output until magnetic saturation occurs. The discussion raises questions about how a weaker armature current induces a stronger current in the stator coils, suggesting that mechanical motion influences magnetic flux and voltage. Factors affecting the current increase include the frequency of the induced voltage and the speed of the armature's mechanical motion. Additionally, the role of self-induction in maintaining voltage until saturation is questioned, particularly in AC generators where rectification is necessary.
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Smaller generators are sometimes self-excited, which means the field coils are powered by the current produced by the generator itself. The field coils are connected in series or parallel with the armature winding. When the generator first starts to turn, the small amount of remnant magnetism present in the iron core provides a magnetic field to get it started, generating a small current in the armature. This flows through the field coils, creating a larger magnetic field which generates a larger armature current. This "bootstrap" process continues until the magnetic field in the core levels off due to saturation and the generator reaches a steady state power output. (Wikipedia)

I have seen similar explanations in more reliable sources, I am assuming this only works in AC generators.

My first question is why/how does a weaker current in the armature induce a stronger current in the stator coils? Does the mechanical motion of the coils in the armature generate a magnetic flux "push/pull" on the electrons in the stator coils thus translating the mechanical motion into increased voltage? Or is that reliant on the winding of the inductor coils?

My second question is by what factor is this increase observed as being?Is that factor reliant on the frequency/current of the returning inducing voltage or the speed of the mechanical motion in the armature? Or are those both factors?

Numero tres, does a self inducting armature generate a higher voltage within the rotor until saturation, or does it simply maintain minus losses to resistance/eddy currents/hysteresis etc. and require feeding from the stator coils?
 
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this is for a series dc generator as Jim said,

In that case, you have slight residual magnetism in your electromagnets in your field, so when your generator is spun at a relatively high speed, it produces a relatively high current in the armature coil, which then flows to excite the field coil, that process continues to winding saturation of your field
 
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