1986, at a final price of $372 million. While thanking the team for their contributions in building the system, the new director of the DOE, John Clarke, also announced that there would be no funding to run it. Clarke later lamented that the decision to cancel the project was very difficult, "It would have been so much easier if I had a technical failure to point to." It sat unused for a year on the chance that operational funding would be provided. It never was. The machine was scrapped in 1987. The DOE also cut funding for most other mirror programs. After 1986 Magnetic mirror research continued in Russia, one modern example is the Gas Dynamic Trap, an experimental fusion machine used at the Budker Institute of Nuclear Physics in Akademgorodok, Russia. This machine has achieved a 0.6 beta ratio for 5E-3 seconds, at a low temperature of 1 KeV. The concept had a number of technical challenges including maintaining the non-Maxwellian velocity distribution. This meant that instead of many high energy ions hitting one another, the ion energy spread out into a bell curve. The ions then thermalized, leaving most of the material too cold to fuse. Collisions also scattered the charged particles so much that they could not be contained. Lastly, velocity space instabilities contributed to the escape of the plasma. In September 2022, University of Wisconsin–Madison researchers incorporated a spin-off startup company named Realta Fusion to develop and commercialize tandem mirror reactors to supply industrial process heat with smaller power plants. Their stated goal is a “lowest capital, least complex path” to fusion energy. Magnetic mirrors play an important role in other types of magnetic fusion energy devices such as tokamaks, where the toroidal magnetic field is stronger on the inboard side than on the outboard side. The resulting effects are known as neoclassical. Magnetic mirrors also occur in nature. Electrons and ions in the magnetosphere, for example, will bounce back and forth between the stronger fields at the poles, leading to the Van Allen radiation belts. Mathematical derivation The mirror effect can be shown mathematically. Assume adiabatic invariance of the magnetic moment, i.e. that the particle's magnetic moment and total energy do not change. Adiabatic invariance is lost when a particle occupies a null point or zone of no magnetic field. The magnetic moment can be expressed as: It is assumed that μ will remain constant