Historical research guide · 1088 · 2012
Tunneling through Coulombic barriers: quantum control of nuclear fusion
Rajdeep Saha · Andreas Markmann · Victor S. Batista
In one minute
Fusing two deuterons means bringing two positive charges close enough to touch, and the Coulomb repulsion between them is a barrier millions of electronvolts high. The usual answer is heat and pressure — hit the barrier hard enough and a few nuclei go over the top. Rajdeep Saha, Andreas Markmann and Victor Batista, at Yale, ask a different question: can you make nuclei go through it on purpose? Their scheme borrows from coherent control and from spin-echo magnetic resonance. A train of low-energy electron-impact ionization pulses, each timed so that it flips the phase of one component of the deuteron’s wavepacket, rearranges the interference between the channels open to that wavepacket. Amplitude is driven into the classically forbidden region under the barrier and out into the fusion continuum beyond. In their simulation the survival probability barely moves without pulses and falls by more than half with them, while the total energy of the system hardly changes at all.
Connection
Chapter 12 treats fusion as the energy substrate the rest of the thesis stands on, and this paper is a clean statement of the site’s central fusion mechanism in ordinary quantum chemistry: the tunnelling rate, not the barrier, is the adjustable quantity. Chapter 2 owns the reason it matters — the pulses do their work by changing the phase structure the wavepacket sees, which is exactly the kind of handle a driven electromagnetic environment offers on a nucleus that is otherwise untouchable.
From the source
The proposal in one line: a train of repetitive low-energy electron-impact ionization pulses can speed up quantum tunnelling of a proton or deuteron through a Coulombic barrier, by acting on the interference phenomena that govern the wavepacket rather than on the barrier itself.Abstract; Section 1 Introduction, closing paragraph
The pulse is a phase kick, not an energy injection. Each electron scattering event transiently carries one vibrational component onto the singly ionized surface and back, and its duration is chosen to produce a phase shift of pi along that component — the unitary operator known as a two-pi pulse in optics and a 180-degree pulse in spin-echo magnetic resonance. Repetitive application of it is the whole control scheme, and it is the same bang-bang dynamical decoupling idea the group had already used with optical pulses.Section 2 Methods and model system, equation 3 with Figure 3
The model is a deuteron in a one-dimensional box two and a half atomic units across — a size set by the plasma density, standing for a deuteron among its nearest neighbours in a dense plasma — interacting with a second deuteron at the origin through the sum of two repulsive Coulomb potentials, with an absorbing optical potential inside the nuclear radius playing the part of the outgoing helium and neutron continuum. The decay of the wavefunction amplitude into that absorber is what counts as fusion. The initial state is the one impulsive ionization of a deuterium molecule leaves behind, and the propagation uses the split-operator Fourier transform method.Section 2, equation 2 with Figure 2
The result: without pulses the survival probability of the bound population decays negligibly. Pulsing every hundred atomic units of time takes more than twenty per cent of the population out through the barrier, and pulsing every five atomic units takes more than half. The slope of the survival curve at early time gives the tunnelling rate and its asymptotic value gives the product yield.Section 3 Results, equation 7 with Figure 4
The energy bookkeeping is the point of the paper. The pulses redistribute population among the levels — destructive interference among bound components, constructive interference inside the barrier and beyond — without significantly changing the total energy of the system, and the energy fluctuations that do appear are of order seven hartree against a Coulombic barrier of order ten to the fifth hartree. Tunnelling proceeds from states below one hundred in the box basis, which is to say from low-energy collisions.Section 3, equation 8 with Figures 5 and 6
What would have to hold for it to be seen, in the authors’ own words: sufficiently high collision cross sections, meaning high density or high temperature, and the survival of quantum coherence over the time scale of the reactive scattering event — the predicted control should be observable unless the decoherence time is much shorter than two hundred femtoseconds. Their suggested application is electron-impact ionization pulsing during the final ignition step of inertial confinement, where they argue it could yield the efficiency gains needed to reach break-even.Section 4 Conclusions and outlook
The way in
https://doi.org/10.1080/00268976.2012.679635How to cite it
Rajdeep Saha, Andreas Markmann, Victor S. Batista (2012) Tunneling through Coulombic barriers: quantum control of nuclear fusion doi:10.1080/00268976.2012.679635