External Field Control Research Articles

Femtosecond pulse dependence of dissipation in molecular systems

Externally applied optical fields may influence molecular dynamics in a direct way alternating the reversible part of the dynamics but also in an indirect manner changing the dissipative processes. This indirect field influence is studied in the framework of the quantum master equation for the density matrix including a field-dependent Redfield tensor. Within a simple model appropriate to describe a dye molecule in solution, the field influence on molecular dynamics is studied for different laser-pulse intensities and lengths as well as bath correlation times. The possible external field control of dissipation is underlined.

External field control of condensed phase reactions

Control of tunneling in a symmetric double well coupled to a bath via an external field is demonstrated. Optimal control theory is employed to design a laser field which couples to the reaction coordinate and drives a localized wave packet on the reactant side to the product side at a specified target time τ. Both a very quantumlike system (high barrier) and a low barrier double well are examined; excellent results are obtained for a range of reduced bath viscosities. Analysis of the control fields and corresponding localization dynamics shows that the frequency components of the control field are more or less in resonance with eigenstates of the double well and that the laser field enhances the natural dynamics of the individual wells. Future extension to more complicated models where the field couples to the bath is discussed.

Cooperating with nonequilibrium fluctuations through their optimal control

The task of fluctuation control in stochastic systems is reformulated as an optimal control problem. We show that it is possible to design an external control field that works cooperatively with system fluctuations to achieve a desired physical objective. The proposed approach is illustrated with one-dimensional Brownian motion as a simple model.

Determining regular orbits in the presence of irregular trajectories using optimal control theory

Two general algorithms are presented to determine regular orbits in the presence of irregular trajectories in a phase space of n degrees of freedom. The first algorithm searches for regular orbits with the energy as a free-floating parameter. The second algorithm seeks regular orbits at constant energy. These two approaches utilize optimal control theory to employ a small external control field that permits a search among the irregular motion for the regular orbits. The optimizing algorithm naturally seeks regular orbits with the control field turned off. Numerical results with a chaotic Hamiltonian show the method to be effective in determining regular trajectories. If the system is completely chaotic in some region, the method determines which initial condition is the best one in order to achieve a nearly regular orbit.

A sharp-boundary dynamical model for a toroidal theta pinch

A set of linear inhomogeneous time-dependent ordinary differential equations is derived to describe the dynamical interaction of the long-wavelength m = 1 instability with the stable oscillations to which it couples. The equations provide an algorithm for determining the plasma response to external feedback control fields. The method is based upon the new Scyllac ordering developed by Weitzner. The results agree with the steady-state equation of Ribe and Rosenbluth. The obtained m = 1 growth rates also agree with previous new-ordering results for a pure ℓ = 0 or ℓ = 2 system, but for a combined ℓ = 0 and ℓ = 2 system the equations have two distinct unstable eigenvalues corresponding to horizontal and vertical growth rates.

Optimal confinement of collisionless plasmas by localized time-varying electric fields†

The problem of optimal confinement of collisionless plasmas by means of external amplitude-limited time-varying electric fields localized to an outer layer enclosing the confinement region (a specified closed bounded spatial domain) is considered. To confine the plasma, the external electric field (control) establishes a finite potential barrier for the escaping particles. The field direction for confinement depends on the sign of the electrical charge of the escaping particles inside the layer. The paper begins with a formal development of the plasma equations. Then, the existence and uniqueness of solutions of these equations are established. This is followed by the formulation of the optimal confinement problem along with a discussion of the existence of an optimal electric field (control). By introducing additional assumptions to simplify the problem, sub optimal feedback controls are obtained. Finally, the effectiveness of the derived feedback controls is determined numerically using a computer-simulated plasma.

A New Technique in Ferrite Phase Shifting for Beam Scanning of Microwave Antennas

A reciprocal ferrite phase shifter for 3-cm wavelength has been developed which makes use of a new design technique for obtaining large phase changes per unit length by electrical means. The device consists essentially of a longitudinal magnetic field applied to a ferrite rod centrally located inside a rectangular waveguide excited in the TE10 mode. With a proper choice of rod diameter and impedance matching elements, phase shifts of greater than 250 ø per inch and variations in transmitted power of less than ±0.2 db have been obtained with external control fields as low as 60 oersteds. Zero-field insertion loss of less than 0.1 db per inch has been measured. These characteristics, along with its geometrical configuration and small size, make this electrically controlled ferrite device useful in the design of rapid-scanning antennas or any similar microwave system requiring phase modulation.