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Register a new userImproved alternating gradient transport and focusing of neutral molecules
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Polar molecules, in strong-field seeking states, can be transported and focused by an alternating sequence of electric field gradients that focus in one transverse direction while defocusing in the other. We show, by calculation and numerical simulation, how one may greatly improve the alternating gradient transport and focusing of molecules. We use a new optimized multipole lens design, a FODO-lattice beam transport line, and lenses to match the beam transport line to the beam source and to the final focus. We derive analytic expressions for the potentials, fields, and gradients that may be used to design these lenses. We describe a simple lens optimization procedure and derive the equations of motion for tracking molecules through a beam transport line. As an example, we model a straight beamline that transports a 560 m/s jet-source beam of methyl fluoride15 m from its source and focuses it to 2 mm diameter. We calculate the beam transport line acceptance and beam survival, for a beam with a velocity spread, and estimate the transmitted intensity for specified source conditions. Possible applications are discussed.
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We have focused and decelerated benzonitrile (C$_7$H$_5$N) molecules from a molecular beam, using an array of time-varying inhomogeneous electric fields in alternating gradient configuration. Benzonitrile is prototypical for large asymmetric top molecules that exhibit rich rotational structure and a high density of states. At the rotational temperature of 3.5 K in the pulsed molecular beam, many rotational states are populated. Benzonitrile molecules in their absolute ground state are decelerated from 320 m/s to 289 m/s, and similar changes in velocity are obtained for excited rotational states. All measurements agree well with the outcome of trajectory calculations. These experiments demonstrate that such large polyatomic molecules are amenable to the powerful method of Stark deceleration.
We report on the focusing and guiding of the van der Waals complex formed between benzonitrile molecules (C$_6$H$_5$CN) and argon atoms in a cold molecular beam using an ac electric quadrupole guide. The distribution of quantum states in the guided beam is non-thermal, because the transmission efficiency depends on the state-dependent effective dipole moment in the applied electric fields. At a specific ac frequency, however, the excitation spectrum can be described by a thermal distribution at a rotational temperature of 0.8 K. From the observed transmission characteristics and a combination of trajectory and Stark-energy calculations we conclude that the permanent electric dipole moment of benzonitrile remains unchanged upon the attachment of the argon atom to within pm5%. By exploiting the different dipole-moment-to-mass (mu/m) ratios of the complex and the benzonitrile monomer, transmission can be selectively suppressed for or, in the limit of 0 K rotational temperature, restricted to the complex.
Neutral particles can be guided and focussed using electric field gradients that focus in one transverse direction and defocus in the other, alternating between the two directions. Such a guide is suitable for transporting particles that are attracted to strong electric fields, which cannot be guided using static fields. Particles are only transmitted if their initial positions and transverse speeds lie within the guides phase space acceptance. Nonlinear forces are always present in the guide and can severely reduce this acceptance. We consider the effects of the two most important nonlinear forces, a term in the force that is cubic in the off-axis displacement, and a nonlinear term which couples together the two transverse motions. We use approximate analytical techniques, along with numerical methods, to calculate the influence of these nonlinear forces on the particle trajectories and on the phase space acceptance. The cubic term alters the focussing and defocussing powers, leading either to an increase or a decrease of the acceptance depending on its sign. We find an approximate analytical result for the phase space acceptance including this cubic term. Using a perturbation method we show how the coupling term leads to slow changes in the amplitudes of the transverse oscillations. This term reduces the acceptance when it reduces the focussing power, but has little influence when it increases that power. It is not possible to eliminate both nonlinear terms, but one can be made small at the expense of the other. We show how to choose the guide parameters so that the acceptance is optimized.
Vertical excursion fixed-field alternating gradient accelerators can be designed with tunes that are invariant with respect to momentum and trajectories that are scaled images of each other displaced only in the vertical direction. This is possible using guiding fields that have a vertical exponential increase, with a skew quadrupole component in the magnet body and a solenoid component at the magnet ends. Because of the coupling this introduces, orbit and optics calculations and optimisation of parameters need to be performed numerically. In this paper, idealised magnetic fields are calculated from first principles, taking into account end fields. The parameter dependence of the optics and the dynamic aperture of the ring are calculated for the example of a ring with an approximately 25 m circumference that accelerates proton beams from 3 MeV to 12 MeV. The paper reports for the first time the design of such an accelerator lattice using tools specifically devised to analyse transverse coupled optics without the need for approximations.
Using calculations and mathematical modeling, we demonstrate the feasibility of constructing a synchrotron storage ring for neutral polar molecules. The lattice is a racetrack type 3.6 m in circumference consisting of two of 180-degree arcs, six bunchers, and two long straight sections. Each straight section contains two triplet focusing lenses and space for beam injection and experiments. The design also includes a matched injector and a linear decelerator. Up to 60 bunches can be loaded and simultaneously stored in the ring. The molecules are injected at 90 m/s but the velocity of the circulating beam can be decelerated to 60 m/s after injection. The modeling uses deuterated ammonia molecules in a weak-field seeking state. Beam that survives 400 turns (15 s), has horizontal and vertical acceptances of 35 mm-mr and 70 mm-mr respectively, and an energy acceptance of plus or minus 2%.
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