Using a kinetic model for the ions and adiabatic electrons, we solve a steady state, electron-repelling magnetic presheath in which a uniform magnetic field makes a small angle α 1 (in radians) with the wall. The presheath characteristic thickness is the typical ion gyroradius ρ i . The Debye length λ D and the collisional mean free path of an ion λ mfp satisfy the ordering λ D ρ i αλ mfp , so a quasineutral and collisionless model is used. We assume that the electrostatic potential is a function only of distance from the wall, and it varies over the scale ρ i . Using the expansion in α 1, we derive an analytical expression for the ion density that only depends on the ion distribution function at the entrance of the magnetic presheath and the electrostatic potential profile. Importantly, we have added the crucial contribution of the orbits in the region near the wall. By imposing the quasineutrality equation, we derive a condition that the ion distribution function must satisfy at the magnetic presheath entrance -the kinetic equivalent of the Chodura condition. Using an ion distribution function at the entrance of the magnetic presheath that satisfies the kinetic Chodura condition, we find numerical solutions for the self-consistent electrostatic potential, ion density and flow across the magnetic presheath for several values of α. Our numerical results also include the distribution of ion velocities at the Debye sheath entrance. We find that at small values of α there are substantially fewer ions travelling with a large normal component of the velocity into the wall.

Recent years have seen great advances in the development of synthetic self-assembling molecular systems. Designing out-of-equilibrium architectures, however, requires a more subtle control over the thermodynamics and kinetics of reactions. We propose a mechanism for enhancing the thermodynamic drive of DNA strand-displacement reactions whilst barely perturbing forward reaction rates: the introduction of mismatches within the initial duplex. Through a combination of experiment and simulation, we demonstrate that displacement rates are strongly sensitive to mismatch location and can be tuned by rational design. By placing mismatches away from duplex ends, the thermodynamic drive for a stranddisplacement reaction can be varied without significantly affecting the forward reaction rate. This hidden thermodynamic driving motif is ideal for the engineering of non-equilibrium systems that rely on catalytic control and must be robust to leak reactions.

Abstract. We develop a gyrokinetic treatment for ions in the magnetic presheath, close to the plasma-wall boundary. We focus on magnetic presheaths with a small magnetic field to wall angle, α 1 (in radians). Characteristic lengths perpendicular to the wall in such a magnetic presheath scale with the typical ion Larmor orbit size, ρ i . The smallest scale length associated with variations parallel to the wall is taken to be across the magnetic field, and ordered l = ρ i /δ, where δ 1 is assumed. The scale lengths along the magnetic field line are assumed so long that variations associated with this direction are neglected. These orderings are consistent with what we expect close to the divertor target of a tokamak. We allow for a strong component of the electric field E in the direction normal to the electron repelling wall, with strong variation in the same direction. The large change of the electric field over an ion Larmor radius distorts the orbit so that it is not circular. We solve for the lowest order orbits by identifying coordinates, which consist of constants of integration, an adiabatic invariant and a gyrophase, associated with periodic ion motion in the system with α = δ = 0. By using these new coordinates as variables in the limit α ∼ δ 1, we obtain a generalized ion gyrokinetic equation. We find another quantity that is conserved to first order and use this to simplify the gyrokinetic equation, solving it in the case of a collisionless magnetic presheath. Assuming a Boltzmann response for the electrons, a form of the quasineutrality equation that exploits the change of variables is derived. The gyrokinetic and quasineutrality equations give the ion distribution function and electrostatic potential in the magnetic presheath if the entrance boundary condition is specified.