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characteristics of the carrier gas. Efficient entrainment can be accomplished using two ovens mounted opposite each other and perpendicular to the supersonic flow of atoms, as illustrated in Figure 1. A temperature gradi- ent in each oven can produce a collimated effusive beam, which can be enhanced by utilizing a continuous flow re- flux design [14]. The ovens are aligned so that atoms that are not entrained into the supersonic flow are de- posited into the opposite oven. This “atomic ping-pong” between ovens greatly reduces the initial amount of mate- rial needed for separation as well as the background pres- sure and the need for recycling through vacuum pumps. Preliminary simulation results show that entrainment ef- ficiencies can be as high as 5-10% of the initial supersonic beam flux [15]. Once entrained, the beam is collimated with a skimmer and propagates into the laser region. The desired isotope will then undergo an irreversible change in magnetic moment, differentiating it from the other isotopes that are unaffected by the laser beam. After in- teracting with the laser, atoms proceed to enter a tube surrounded by multipole magnets, which produce a mag- netic gradient that guides low-field seeking atoms and anti-guides high-field seeking atoms [22]. 

The force due to the inhomogeneous magnetic field is F = µ$_{B}$g$_{J}$m$_{J}$ ∇ B , where µ$_{B}$ is the bohr magneton, g$_{J}$ is the Lande-g factor, m$_{J}$ is the projection of the total an- gular momentum on the quantization axis, and ∇ B is the gradient of the magnetic field. The maximum magnetic field of the gradient would be strong enough to cause a few elements, such as lithium, to enter the Paschen-Back regime. Most of the periodic table, however, would re- main in the weak field limit because of the strong LS coupling present in heavier atoms. 

Lithium serves as a simple example because it has two stable isotopes, $^{6}$Li and $^{7}$Li, with natural abundances of 7.6% and 92.4% respectively. In our proposed exper- iment, illustrated in Figure 1, lithium is entrained into the supersonic beam, and a 670.96 nm laser tuned the $^{7}$Li D 2 -line (2 $^{2}$S$_{1}$$_{/}$$_{2}$ (F=2) → 2 $^{2}$P$_{3}$$_{/}$$_{2}$ (F=1 or F=2)) optically pumps the $^{7}$Li into a high-field seeking state. The laser depletes the $^{2}$S$_{1}$$_{/}$$_{2}$ F=2 manifold and optically pumps all of the atoms into the $^{2}$S$_{1}$$_{/}$$_{2}$ F=1 manifold. At fields greater than about 50 G, the entire F=1 manifold be- comes high-field seeking. This process allows us to effi- ciently pump all of the unwanted $^{7}$Li atoms into an anti- guiding mode using a single laser wavelength. Since we do not excite $^{6}$Li, we take a statistical loss of one half of the $^{6}$Li due to the magnetic sub-level projections. Fig- ure 2 shows the radial distributions of the two lithium isotopes entering the magnetic guiding region, as well as their distributions upon leaving the tube. The isotope- selective guiding and anti-guiding are clearly evident, and the enrichment can be made arbitrarily high by optimiz- ing the geometry of the tube. Once an atom collides with the tube walls, the simulation assumes it sticks. 

The results of Figure. 2 were simulated assuming a 

0.5 m long region of quadrupole guiding magnets whose specifications are discussed below. That geometry yields 95% enrichment of $^{6}$Li, and 36 . 8% of the $^{6}$Li that enters the guiding region survives to be collected. The simula- tion assumes a beam with a mean velocity of 800 m/s and an initial Gaussian spread of 15 m/s in each component of the beam velocity. This velocity corresponds to entrain- ing lithium into a beam of helium. The skimmer shown in Figure 1 is 5 mm in diameter, and approximately 10% of the beam survives it and enters the multipole tube. 

We simulated a quadrupole magnetic field produced by four permanent magnets for the separation of lithium. The magnets are 1 $_{2}$” × 1 $_{2}$” × 1” and have a residual flux density of B r =1.48 T. The magnets surround a 1.5 cm inner diameter (1.6 cm outer diameter) stainless steel tube. The resulting magnetic flux density, illustrated in Figure 3, was simulated using finite element analysis. We chose this geometry to avoid putting the magnets in 

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