Axial trapping force

Keywords— laser beam effects, optical fiber, optical trapping, axial trapping force, theoretical analysis, refractive index. 

Fig. 7. Schematic diagram of forces exerted on a cell when using an inverted microscope with (A) epi-illumination (i.e., laser focused through the objective) or (B) transillumination (i.e., laser focused through the condenser). is the axial force, and Fl is the lateral trapping force. Curved arrows represent the laser beam waist and point in the direction of light propagation.

In the axial direction the recoil force is many orders of magnitude larger than the axial dipole force. The potential minimum with respect to the radial dipole force is E ot — —5 x 10 eV. In order to trap atoms in this minimum their radial kinetic energy must be smaller than 5 x 10 eV, which corresponds to the temperature T 5 x 10 K. 

The ion trap works on a similar principle to the linear quadrupole. Oscillating RF and DC voltages are applied to the electrodes. These voltages create a quadrupolar field in the ion trap, and ions can be retained in stable trajectories in this field. The force acting upon the ions in the trap is directly proportional to the distance of the ions from the center of the ion trap. Therefore the quadrupolar field acts to store the ions as a packet at the center of the trap. For an ion to be retained in the ion trap it needs to have a stable trajectory in both the axial (z) and radial (r) directions. Whether the ion is stable in one or both of these directions is given by the solutions to the Mathieu equation previously used to describe ion motion through the linear quadrupole with the reduced Mathieu parameters ... 

The relative efficiencies of trapping absorbing particles using Gaussian beams and doughnut beams can be measured in terms of the ratio of the radial force to the axial force. As can be seen from Figure 8, the doughnut beam trap has smaller axial forces for trapped particles. 

The efficiency of the trap can be measured by the ratio of the radial force to the axial force. These ratios are calculated here for beams of waist size 2 pm and power of ImW. The particle has a radius of 1 pm and is in a plane 30 pm before the waist. 

By ramping tbe rf voltage V, ions of successively increasing m/z are forced to adopt unstable trajectories and are ejected out of the trap in the axial direction for external detection. 

Compressors fall into one of two fundamental types - positive displacement and turbo-machines. Positive displacement machines can be either rotary or reciprocating. They both trap the gas in a cylinder and then force it into a smaller volume and so increase its pressure. Turbo-machines impart velocity to the gas and its momentum carries it into a narrowing space and so its pressure increases. Turbo-machines can be either axial (in which the flow is parallel to the shaft) or centrifugal (in which the flow is at right angles to the shaft). Multistage turbo-machines, with intercoohng, are common. 

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