Biomedical Engineering Reference
In-Depth Information
(b)
(a)
(c)
Figure 4.13
RandomwalkBField-inducedeffects.(a)Positionaloffsets,(b)
velocity magnitude and (c) velocity parallel and orthogonal to the
z
axis.
of the velocity and force components parallel and transverse to the
applied B field.
Assuming both an E field and a B field is involved, a Lorentz
equationforthemotionoftheionbetweencollisionsmaybewritten
where,likeotherrandomwalkmodels(Reif,1965),noviscousterm
exists.
m
d
d
t
=
qE
+
q
v
×
B
(4.4)
Whereas the viscous model lumps the entire collision process
into a viscous term, the random walk model inserts each collision
explicitly. The walk is constructed by generating random thermal
velocitiesaftereachcollision.Randomnumbersallocatethethermal
velocitiesthathaveaGaussianprobabilitydistribution.Thecollision
periods having a Poisson probability distribution are also randomly
selected, the user specifying the average collision rate. The Lorentz
equations are solved analytically to yield the current position after
this period, and a collision is then assumed to occur. The process is
now repeated until the desired total time has elapsed. The result is
