L1 to L3 are basic storage inductors. Main parameters are inductance, saturation current, DC resistance, AC losses.
Flux is primarly related to voltage integral, not current. You have to go into inductor detail design to see the implications.
Typically more abrupt saturation than ferrites, parameters are however different. Refer to datasheets.
I found it, they are used as magnetic amplifier chokes. That is why they have only one winding on them. Now, that is a good source of these special properties cores.
Text from a brochure:
The heart of a Mag Amp-choke is a toroidal core made from
a soft-magnetic alloy with rectangular hysteresis loop and, in
most cases, just one winding for operation and control
currents. The specification requirements with regard to choke
material are very high. In addition to low magnetic reversal
losses (effect on heat build-up, control current, efficiency), a
markedly rectangular hysteresis loop featuring high
remanence (effect on control range) and good saturation
behaviour is required. For this reason, amorphous Co-based
alloys such as VITROVAC 6025 Z have been accepted
worldwide as ideal materials for this application.
The function of the Mag Amp can be described as a high
speed on/off switch similar to a switching transistor. The
rectangular B-H loop is causally related to two operating
states. The switch is open as long as the choke is
magnetized and the current flow to the output is blocked. As
soon as the core material is saturated, the switch is on and
current starts to flow to the output. This effect is based on a
rapid change in impedance IZI (or inductivity L or
permeability µ) of the choke across 3-4 orders of magnitude
when going into saturated condition.
This switching function is used for pulse width control of the
voltage pulse induced in the respective secondary winding
(before this pulse is rectified and smoothed by the output
filter).