That is not the way in fact, the device oh Hans Coler does not use bi-filiar coils (Aryton-Perry), it uses two opposite coils to produce resonance:

Principle experiment of a ZPE-flux accelerator.
A copper coil which is crossed through the core. As a core can be used instead of iron and another metal, or a plasma stream.
The accelerated ZPE magnetic flux is directed to the right in the right-hand rule and the carrying core.

ZPE magnetic flux acceleration at current-carrying coil (iron core) = 100%
ZPE magnetic flux acceleration after 20 millisec. Cut-off = 93%.
When a pulsed coil flows through the magnetic field an accelerated decreases its power consumption.
Thus, the two opposed coils each magnetized with less power consumption.

Oscillator with two acceleration coils
Also referred to as non-inductive coil or Biström oscillator.
The two coils oscillators must be identical and equally strong.
You are connected as a bridge phases twisted together.
The magnetic cores or tube amplifiers operate as ZPE flux accelerator with pulsating direct current, not alternating current. Therefore, at least two separate magnetic flux accelerators are needed for a self-oscillating current generator, the pulses alternately as a bridge.

When a magnetic flux flows in parallel to an electrical conductor, the speed is multiplied.
When a magnetic flux flows in parallel to an electrical conductor, its electrons are loaded (doped), and generated from the particles present as Helion 1 and 2, a centrifugally accelerated magnetic (Protons) flow. Wherein the magnetic flux is concentrated and accelerated.
It arises in the conductor due to the excess magnetic Protons flow. This flow differs due to lack of space from the middle to both ends, moves according to the (right-hand rule) as a spiral around the conductor and radiates.
The two coils with a capacitor to vibrate at its natural resonance.
The two coils can be wound on a core side by side.
See cyclone generator:
The poling direction of the magnetic field is unimportant, because the field is flowing slowly.
The field from the next smaller particles (deutron) circulates inside as giving power.
The Double ball-and-egg cascade of crop circles.
The cascade is doubly symmetric, because it resonates as Biström oscillator, and both sides thus magnetized by a current flow.
The core, which should lead to accelerated magnetic flux
1 The tungsten coil found in Balbanju / Ural Russia consists of bundles thread-shaped tungsten geradelienigen crystal structures with a single thickness of the order of 1 micron. Behold: Phaser.
2 Ferrite.
3 directed soft iron (NANOPERM see MEG) www.magnetec.de / nanoperm_e.htm .
4 Electrically conductive permanent magnet (Alnico).
5 annealed and directed iron rod.

Non-inductive coils are connected as a bridge used in the current generators.
Rock on, and then produce itself current.

I guess is possible to build a resonant circuit using in some parts a inductance cancelled, and Aryton-Perry is a type of bi-filiar winding, the thing is the device Hans Coler use a work system wich is very difficult to understand.

The apparatus was tested in 1926 by Professor M. Klose from the Technische Hochschule Berlin-Charlottenburg and Professor WO Schumann of the Technical University of Munich, who confirmed that it was working properly, but were not able to explain how the energy was produced.

Franz Haid of Siemens-Schukert could replicate it, the device was seen by Dr. Kurt Mie of Berlin Technische Hochschule and Herr Fehr (Haber’s assistant at the K.W.I.) who reported that the device apparently worked, and they could detect no fraud.

it is right wikipedia is wrong about Ayrton-Perry (they said it), but why the image of above is non-inductive bi-filiar coil and the second one (Nikola Tesla's bifilar coil) is inductive? (both are bi-filiar)

http://en.wikipedia.org/wiki/Bifilar_winding

That coil has an adjustable ratio of mutual versus leakage inductance.