r(mirror) = Bmax/Bmin
a particle will be reflected by a magnetic mirror if v(perpendicular)/v(parallel) > 1/sqrt(r(mirror))
In a high beta reactor the magnetic field is excluded from the body of the plasma, giving a near zero Bmin. Cusp effects that are negligible in a low beta mirror come to dominate losses.
This is flawed reasoning I think, or at least applied in an inappropriate fashion.. It is referring, I think, to B field gradient change. If the B flield gradient is unchanged the charged particle will spiral along the field line for ever without reversing. But if the gradient increases(like near poles or locally stronger magnets or magnets closer together, the particle may mirror. The center of the gyro motion remains the same (same B field strength), but the rate of change on either side of this B field line is greater and this leads to the mirroring. I may not be making much sense, but what I am implying is that the above Bmax/ Bmin expression refers to this gradient as the charged particle gryrates along a fixed B field strength field line. The greater the parent magnet strength and / or the closer two opposing magnets are the greater is this gradient as you approach a pole or closest approach between magnets.
With the Wiffleball border, this spiraling motion with mirroring does not apply to any significant amount. The particle completes only ~ 1/2 of a single gyro orbit before it reenters a B field absent region. No spiraling, no chance for the mirroring effect to manifest. The behavior is essentially like bouncing off of a hard wall. The geometry of the particle bouncing of of these walls determines whether it will return to the interior or ricochet through the cusp.
Bmin essentially does not approach zero, it is zero, and the equation becomes meaningless. Zero in the sense that it's effect is greatly dominated by other interactions like space charge, collisions, and inertia.
Let me try again. Bmax/ Bmin , in a constant B field would be 1/1. I think everyone would agree that no mirroring would happen here. If you were talking about the motion of a charged particle perpendicular to the field, the constant strength would turn the particle with a given constant radius of curvature. How this particle reached this B field region is ignored, it is just there. There is also a lateral displacement depending on B field strength, mass and Z and polarity. A constant spiraling velocity with a fixed frequency and perfectly round orbit occurs. If this B field strength is greater or lesser, nothing changes except this constant orbit radius and associated frequency. No slowing or reversal, no mirroring. You have to consider variable B field strength relative to the reference gyroradius mid line reference point. Here if this variance is constant the gyro orbit will become parabolic, not perfectly circular, but so long as this relative strength variation is constant so is the spiraling motion. If this variation changes along the path of the spiraling axis though, things change. The gyro orbit becomes more parabolic. For some reason this increases the frequency, slows the lateral motion and can eventually reverse. I don't know why except to invoke the magic term Lorentz force. The B max/ Bmin refers to the B field strength on the inner edge and the outer edge of the gyro orbit and thus the radius of the gyro orbit of that specific orbit. Progressive spiraling orbits enter regions where this inner to outer B field strength ratio becomes greater. I'm supposing that the increasing parabolic shape counterbalances the total orbital excursion so that the gyro orbit radius looks unchanged. But like planets in parabolic orbits, less volume is swept out so orbital speed (orbits per second) can increase. Eventually forward motion ceases. There is no reason to reverse, except due to chaotic(?) motions, if the particle moves slightly backwards it has less KE and thus travel down the potential well commences. There is a limit where the differential between the inner and outer B field strength gradient breaks down, Here the outer parabolic portion of the orbit becomes so great that the particle escapes the B field dominance and other influences dominates. This is represented by the Wiffleball border.
Another perspective- Arrange constant B fields parellel to each other, each successfully stronger. Introduce a charged particle with a given KE to the weakest field, it assumes a given gyroradius and spirals into the second stronger field, its gryroraduis shrinks and frequency increases, continue this process till the gryoradius is very small and the frequency is very high, The forward spiraling motion per orbit slows, till eventually it is so small that it can randomly reverse with out having to overcome a significant energy barrior, now it unwinds in the opposite direction. This is mirroring. I think the magnetic field is transferring energy to the particle during wind up and recovering it during wind down. The net effect is that the particle is confined, without net energy loss (ignoring gyrotron radiation losses).
This rumination, perhaps nonsensical, is a consequence of the last quoted statement, but perhaps I am merely obsessing with the terminology. Mirror machines have cusps. Mirroring is just the mechanism for a magnatized plasma to avoid those cusps for a time. If by "cusp" losses they refer to plasma escape due to mechanisms not related to mirroring it makes sense. But, it seems to imply that this cusp confinement is worse than mirror confinement. That need not be the case. Another way of stating it, perhaps more relevantly is that:
Cusp Confinement in High Beta conditions is mechanistically different than mirroring. And this mechanism can be more efficient at containment than mirroring mechanisms.