A charged particle trap having a spherical shell of magnetic material and apherical hollow cavity positioned concentrically within the shell. A polar axis passes through the center of the shell and cavity. The shell is permanently magnetized to produce a double-tapered magnetic field having barrel-shaped flux lines that are concentrated at the cavity poles. The magnetic material has a remanence B.sub.r (&thgr;) that varies in direction and magnitude such that its angular orientation &agr; with respect to the polar axis varies as a function of the polar angle &thgr; of the material's average location in accordance with the equation &agr; =2&thgr;. The magnitude of the remanence B.sub.r (&thgr;) varies according to the following expressions: B.sub.r (&thgr;)=B.sub.r (0) [B. sub.r (&pgr;/2)-B.sub.r (0)] 2&thgr;/&pgr;, for average polar angles between &thgr;=0 radians and &thgr;=&pgr;/2 radians; and B.sub.r (&thgr; ) =B.sub.r (&pgr;/2) [B.sub.r (&pgr;/2)-B.sub.r (0)] (2&thgr;-&pgr;)/&pgr;, for average polar angles between &thgr;=&pgr;/2 radians and &thgr;=&pgr; radians. An equatorial access port passes through the shell and communicates with the cavity. Charged particles entering the cavity via the access port will normally be deflected by the magnetic field into helical paths about the flux lines. As these particles approach the cavity poles, concentrated magnetic fields will cause them to spiral into ever-tightening helixes until they are reflected back into the central region of the cavity where the process repeats.
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