The French Z-machine
Mathias Bavay's Thesis
Document published online on June 17, 2006
You can find this highly documented thesis at:
http://mathias.bavay.free.fr/these/sommaire.html
Title:
Magnetic flux compression in a sub-microsecond regime for achieving high pressures and X-ray radiation
Defended on July 8, 2002, at CEG (Military Experimental Center of Gramat, Lot).
The Gramat generator (see images above) is capable of delivering current pulses of 2.5 million amperes, lasting 800 nanoseconds.
Gramat ECF Electrical Generator
A close-up view shows the installation's diameter, approximately 20 meters (compared to 33 meters for Sandia's Z-machine).
Close-up View
Central part of the Gramat ECF installation
The setup conceived by Bavay, tested at Gramat and on Sandia's generator, is highly original. The Soviets had previously developed flux-compression systems where a chemical explosive exerted pressure on a "liner" made of electrically conductive material—copper or aluminum. This liner imploded, compressing a magnetic field previously established inside it via an electrical discharge through a solenoid powered by a bank of capacitors. The idea developed in Bavay's thesis consists in using a wire-based liner as a "piston," replacing the external chemical pressure used in magneto-cumulation compressors with "magnetic pressure." Two key concepts emerge:
- Use a lighter liner with lower inertia
- Ensure all energy is transferred to it, since the "magnetic gas" has "zero inertia."
This leads to a two-stage compressor with... two liners, one large and one small. This is essentially what would have been achieved with Sakharov's plasmoid gun if... the gun had been sealed!
Modified Sakharov Plasmoid Gun
We return to the initial scheme. An electrical discharge creates a magnetic field in the "chamber" A. Then, the explosive on the left is detonated, causing the copper liner to expand.
The copper cone seals the chamber, trapping the magnetic field, which, when compressed, tends to expel the aluminum ring into the space between the copper "barrel" and the central explosive-filled liner. But in this new configuration, we prevent the expulsion of the ring, which then impacts at high speed the closed end of the "barrel," generating intense pressures. Of course, we have evacuated the space between the copper ring and the right-side obturator, shown in gray. The aluminum ring acts as a second "liner," vaporizing and transforming into plasma as it passes through. The central liner also undergoes plastic deformation.
Returning to Bavay's thesis, we will recognize elements from the above setup, but constructed differently. As mentioned, both liners are "wire-based" and will transform into plasma. A certain magnetic pressure must be established inside chamber A before it is sealed. The propelling element—the gas from the explosion—must be replaced by magnetic pressure. We then obtain the following:
Bavay's Thesis Setup
To better understand, it might help to merge the two stages shown here into a single image. First, here is Bavay's setup in its initial state:
Mathias Bavay's Setup in Initial State
There are two electrical discharges: one represented in violet, the "primary discharge," and the other in red, the "secondary discharge." These two discharges generate magnetic fields within two coaxial, toroidal-shaped cavities. A cylindrical liner is visible, actually composed of a first set of wires. Bavay's thesis reveals that when these wires carry a strong electric current, they do not instantly transform into metallic plasma. On the contrary, they have a relatively long lifetime, reaching up to 80% of the time it takes for this "wire curtain" to move radially inward toward the axis. This is precisely the secret behind maintaining axisymmetry in Sandia's experiments. When this structure implodes, it is neither a set of wires placed side by side nor a plasma curtain, but a "mixture of both." This phenomenon was theorized by Malcolm Haines, who calls it "shell formation":
Shell Formation
At the top, shortly after the discharge initiation, the wires are still visible. They begin to sublimate superficially. These still-solid wires are surrounded by a sheath of metallic plasma. Bavay's thesis states that the wires retain a cold, solid core. They vaporize at their periphery, emitting a plasma composed of metallic atoms that spreads outward. When these plasma cylinders meet, the "crown" forms. Bavay notes that this crown forms when 80% of the implosion time has elapsed. This means that for the entire duration, current flows individually through the wires. While MHD instabilities can arise in a plasma (ionized gas) where local current density and magnetic field intensity may fluctuate, this is not the case in a wire curtain.
Bavay's thesis reports that the expansion velocity of the metallic vapor is 10,000 m/s for tungsten and 22,000 m/s for aluminum. The approximate diameter of the wires (numbering 240) is 10 microns.
I could not find the expansion velocity for stainless steel wires. The Sandia team was greatly surprised to discover that the temperature reached at the end of the implosion was 2 billion degrees. One possible explanation is that the expansion velocity of stainless steel vapor is lower, delaying the formation of the "crown" where instabilities might arise. As previously noted, the wires maintain a "cold core," meaning that it is essentially "wires" that meet at the axis, with the plasma filament forming only in the final moments of implosion. Thus, instead of hundreds of km/s, the radial velocity at impact could reach 1,000 km/s. Hence, this temperature rise is linked to a... material change. Open question.
At time tm, the plasma sheaths merge. This achieves two objectives. This closure creates an "impermeable barrier" against the magnetic field, while the azimuthal non-uniformity of the medium opposes the growth of MHD instabilities and maintains axisymmetry of the process.
Returning to Bavay's schematic, after having refined it:
Bavay's Setup After Crowbar
In this discharge, capacitors discharge into circuits with inductance. For those who can visualize in 3D, the distributions of the two violet and red current sheets have the geometry of the generating curves of a torus. They are "sorts of inductors." When the "wire + metallic plasma" curtain has progressed toward the axis, it closes what Bavay calls a "gap." In doing so, this "inductor" becomes isolated from the capacitor that charged it. We encounter again the theme of the crowbar, mentioned earlier in this dossier. The red electric current will continue to...