Similar ripples in bifilar coils have been documented on the webpage "Nuclear magnetic resonance of certain materials in the inductor" at the "Research website of Vyacheslav Gorchilin". He attributes it to Nuclear Magnetic Resonance (NMR).
In my opinion, the real reason for the ripple is Electron Dia-magnetic Resonance. Paired electrons have coupled magnetic fields, which form a magnetic ring, similar to attaching two horseshoe magnets to each other.
A uniform magnetic field exerts no magnetic force on such a magnetic ring when that magnetic ring is devoid of leakage flux. However, a current which passes through the ring can exert a torque on it.
When you apply a pulsed high voltage to a coil, you create a strong pulsed electric field through the insulation. The changing electric field produces an electric displacement current which passes through the atoms of the insulation. Then the paired electrons, with their ring-shaped magnetic fields, attempt to oppose the change of electric field by changing the orientation of their magnetic ring. Because of the weak diamagnetic response, the electric fields generated by the paired electrons oppose only about 1 part in 100,000 (or 10^-5) of the applied electric field.
However, if you have in addition to these pulse fields another field, but a steady one, that is a DC magnetic field of, say, 0.5 gauss, then what may happen? What happens is that the electrons in the pair, which have opposite spins and opposite magnetic moments, will experience opposite magnetic torques by that magnetic field. Therefore, they will precess at an angular frequency that depends on the ratio of the magnetic torque to the angular momentum. As a result, the symmetry axis of the magnetic rings in each atom will precess at right angles to the applied steady DC magnetic field.
The magnetic ring of an electron pair possesses both a toroidal magnetic field and a "poloidal" magnetic vector potential. By rotating the symmetry axis of the magnetic ring about an axis aligned with the DC magnetic field, one generates a rotating "poloidal" electric dipole perpendicular to both:
1) the applied DC magnetic field
2) the symmetry axis of the magnetic ring.
So for instance, suppose you applied an RF electric field of 100 volts / mm through the wire's insulation. This could be produced in effect by any adequately fast and intense pulse discharge as it so happens that rapid discharge pulses contain waves at a multitude of RF frequencies according to the mathematics of the Fourier transform.
Let the insulation's relative magnetic susceptibility be -0.00001 or -1.0*10^-5, which is about typical for many solid materials. 100 volts AC / mm multiplied by 10^-5 equals 1 volts AC / meter. 1 volts AC / meter is the insulation's diamagnetic EMF in response to the AC magnetic flux generated by the displacement current due to the 100 volts AC / mm electric field. However, the 1 volts AC / mm is a rotating electric field residing inside the insulation, and is generated by the rotating magnetic rings of the paired electrons of that insulation.
Therefore, after 1 quarter of a cycle of rotation past the time of peak applied electric field, the diamagnetic EMF will have rotated about the DC magnetic field axis to be parallel to the wire, instead of perpendicular. Thus, the insulation then behaves as a resonant dielectric wire which emits radiofrequency (RF) energy which is captured by electrons in the copper wire. The emission is effectively in the electromagnetic far-field regime as long as the skin depth is some fraction of the thickness of the wire. See the article section about "Speed of electromagnetic waves in good conductors" on Wikipedia to extrapolate why this effect is in the electromagnetic "far-field" and not the electromagnetic "near-field". This energy comes from the embodied kinetic energy of the paired electrons, which becomes "mechanically-available" when they provide a mechanical means by which to extract said energy, in the form of a "diamagnetoelectrically" induced rotating dipolar electric field.
Because the energy transfer occurs via the electromagnetic far-field, the electric current in the copper does not have to pass through the magnetic rings of the paired electrons in order to acquire their energy. Detached loops of electric field are jettisoned outward away from the rotating magnetic rings' orthogonally-induced rotating electric dipoles inside the insulator, and these electric loops (which are geometrically "poloidal") are captured by the copper wire and "squished" inside the copper itself, manifesting as an electric wave whose phase varies with the depth from the copper wire's surface (i.e. the "skin effect"). The response of electrons in the copper wire is to jettison their own looped electric fields, which are also geometrically "poloidal", and these electric field loops propagate into the insulation and exert an EMF onto the "poloidal" currents of the electron pairs. These "poloidal" currents are same ones responsible for the electron pairs' toroidal magnetic flux rings. Thus, in effect the inductive energy contained in the magnetic flux rings of these paired electrons is harnessed. The inductive energy is sustained by the embodied kinetic energy of the paired electrons, which in turn is sustained by the so-called "zero point field" which is responsible for maintaining the values of fundamental constants, such as the individual mass of an individual electron.
The rotation (or, rather, "continuous flipping") frequency of the magnetic rings of the paired electrons depends on both the magnitude and orientation of the applied DC magnetic field. At a magnetic field of 0.5 gauss, the magnetic rings will rotate at a frequency of 1.4 MHz. There exists both an axial applied magnetic field and a radial applied electric field (per cylindrical coordinates) between each turn of the bifilar coil. The source of the axial magnetic field between the winding turns may be a permanent magnet or simply due to the current in the coil. As the current in the coil changes, this may cause a shift in the magnetic field, thus affecting the precession frequency. Earth's magnetic field strength may play a role in some cases causing this frequency shift to be negligible in the case that Earth's magnetic field strength exceeds that of the coil's own magnetic field strength. In the event that both the applied magnetic field and applied electric field are reversing every half-period, the output voltage generated by the rotating magnetic rings is a pulsed DC, which agrees with the waveforms observed and documented by Vyacheslav Gorchilin in his article "Nuclear magnetic resonance of certain materials in the inductor".
In a Joseph Newman machine consisting of a 9000-lb (or 4 metric ton) copper coil inductor with a 700-lb (or 300 kilogram) ceramic magnetic rotor, which was analyzed by Dr. Roger Hastings (Reported in the article: "MEASUREMENT & ANALYSIS OF JOSEPH NEWMAN'S ENERGY GENERATOR"), the measured magnetic moment of the permanent magnet rotor was "100 Tesla-cu.in" which is equivalent to 1304 ampere meter^2. So at the 2 foot radius of the heavy 9,000 lb coil, the applied field from the rotor would be 5.8 gauss, thus inducing electron precession at a frequency of about 16 MHz, which is in good agreement with the 13 MHz RF observed by Dr. Roger Hastings.
It is important to note that in Newman's machine, the mechanical commutator's capacitive discharge energy is not shunted to ground but rather is propagated transiently along the length of the inductor coil's copper wire. Due to the sudden change of voltage at the edge of the transient wavefront, it is at these very wavefronts that the high-intensity RF electric fields can be found. This is because the inductor coil behaves as a transmission line such that the rate of change of the electric potential over time shows as a gradient of the electric potential over the length of the copper wire, and consequently as a radial electric field existing between consecutive copper winding layers of the inductor coil (per cylindrical coordinates). The radial electric displacement current leading the center of the transient is reversed that of the radial electric displacement current lagging the center of the transient. Consequently, the frequency of that radial electric displacement current is directly tied to the propagation of that wavefront through the consecutive winding layers of the inductor coil. The electrons that are ahead of the transient's center experience supportive EMF and are carried forward like a surfer catching a breaking wave. Due to the limited speed of electrons, that energy is transported to the electrons even further ahead of the wavefront through the longitudinal "hydraulic effect" that electrons in a copper wire have on each other. Thus the energy acquired by the wire continues to be built upon as the transient progresses through the successive winding layers of the inductor coil.
Since only a tiny fraction of the Newman machine's coil inductor is subject to this high-intensity RF electric field at any one time during the propagation of the transient, only a tiny percentage of the 9000-lb (4 metric ton) coil is exploited for the generation of power, which according to me, as I explained in detail above, is due to Electron Dia-magnetic Resonance (EDR). The transient is reflected multiple times from both ends of the Newman Machine's coil inductor, and during the several hundred microseconds between each reflection it gains additional voltage (suggesting an increase in capacitive energy), which is observed as multiple additive discrete voltage steps at the oscilloscope probe end, revealing a graph with a deep reverse voltage flyback spike with a deep "staircase" consisting of many steps, as revealed in Hastings' report.
If the magnetic field of the inductor coil is enhanced by a material such as iron and whose leakage magnetic flux directly acts on the wire of that coil, the precession frequency of the electrons will be so high (>100 MHz) that the skin effect will suppress any acquisition by copper wire of the >100 MHz RF energy released from the paired electrons of the insulation covering the copper wire. If, on the other hand, the iron is wrapped with the inductor coil and flux leakage is all but eliminated, there still remains a magnetic hysteresis power loss which may exceed the power released from the paired electrons, obscuring any benefit from the Electron Dia-magnetic Resonance, especially at these high frequencies.
It must also be noted that if the circular diamagnetic polarization of the electron pairs' magnetic rings saturates, then there would exist a limit to the electric field generated by the continuous flipping of the magnetic rings - that is - with respect to any given frequency, such that the power transfer to the copper wire may be in useful amounts only above some high frequency, say, 1 MHz.