Efficiency of molecular machines with continuous phase space

We consider a molecular machine described as a Brownian particle diffusing in a tilted periodic potential. We evaluate the absorbed and released power of the machine as a function of the applied molecular and chemical forces, by using the fact that the times for completing a cycle in the forward and the backward direction have the same distribution, and that the ratio of the corresponding splitting probabilities can be simply expressed as a function of the applied force. We explicitly evaluate the efficiency at maximum power for a simple sawtooth potential. We also obtain the efficiency at maximum power for a broad class of 2-D models of a Brownian machine and find that loosely coupled machines operate with a smaller efficiency at maximum power than their strongly coupled counterparts.Comment: To appear in EP

Possibilities for reduction of transverse projected emittances by partial removal of transverse to longitudinal beam correlations

We show that if in the particle beam there are linear correlations between energy of particles and their transverse positions and momenta (linear beam dispersions), then the transverse projected emittances always can be reduced by letting the beam to pass through magnetostatic system with specially chosen nonzero lattice dispersions. The maximum possible reduction of the transverse projected emittances occurs when all beam dispersions are zeroed, and the values of the lattice dispersions required for that are completely defined by the values of the beam dispersions and the beam rms energy spread and are independent from any other second-order central beam moments. Besides that, we prove that, alternatively, one can also use the lattice dispersions to remove linear correlations between longitudinal positions of particles and their transverse coordinates (linear beam tilts), but in this situation solution for the lattice dispersions is nonunique and the reduction of the transverse projected emittances is not guaranteed.Comment: 13 pages, 2 figure

Optimal Twiss Parameters for Emittance Measurement in Periodic Transport Channels

Our objective in this paper is to describe an invariant optimality criterion and then apply it to the procedure of emittance measurement in periodic beam transport channels.Comment: 3 pages, IPAC1

Relations between Projected Emittances and Eigenemittances

We give necessary and sufficient conditions that two sets of positive real numbers must satisfy in order to be realizable as eigenemittances and projected emittances of a beam matrix. The information provided by these conditions sets limits on what one can to achieve when designing a beam line to perform advanced emittance manipulations.Comment: 3 pages, IPAC1

Invariant Criterion for the Design of Multiple Beam Profile Emittance and Twiss Parameters Measurement Sections

We introduce and give examples of applications of an optimality criterion which can be used for the design and comparison of multiple beam profile emittance and Twiss parameters measurement sections and which is independent from the position of the reconstruction point.Comment: 3 pages, IPAC1