Environmental Engineering Reference
In-Depth Information
Figure 6.5 Parameters of motion of a trapped
ion along a closed trajectory:
coordinate of the point where the resonant
charge exchange event proceeds, and θ is
the angle between the direction of ion motion
after charge exchange and vector R .
r min is the min-
imum distance from the particle,
r max is the
maximumdistancefromtheparticle, R is the
point, which becomes the ion energy, and the angle
between the atom velocity
and vector R . We consider below the region of action of the particle field,
θ
j
U ( R )
j ε
,
(6.42)
from which a forming ion cannot move from the region of action of the particle
field. Therefore, after a subsequent resonant charge exchange event it can transfer
to another close trajectory or fall to the particle surface. As a result, a self-consistent
field U ( R ) is created on the basis of the Coulomb field of the negatively charged
particle, and on the basis of fields of free and trapped ions.
Let us find the number density of trapped ions N tr that follows from the balance
equation
N a
σ
res N i P tr v i
D
N a
σ
res N tr v tr (1
p tr ) .
(6.43)
Here N i is the number density of free ions,
v i is the relative velocity for a free ion
and atom partaking in the resonant charge exchange process,
tr is the relative ve-
locity of a trapped ion and atom, P tr is the probability of forming a trapped ion
as a result of resonant charge exchange involving a free ion, and p tr is the prob-
ability for a trapped ion to remain in a closed trajectory after the resonant charge
exchange. If we assume v i
v
1, we obtain from (6.43), the
same order of magnitude for the number densities of trapped ions as for free ions
in the region of action of the particle field. Then the smallness of the probability
of resonant charge exchange for a free ion because of a low density of buffer gas
atoms is compensated for by the long lifetime of trapped ions compared with the
flight time of free ions in the region of action of the particle field.
In analyzing the balance equat ion (6.43) u nder conditions (6.42), we note that
the velocity of a free ion is v i
v tr , P tr
1, and p tr
<
D p 2
/ M in this region. Assuming the particle
field to be close to that in the Coulomb field, we obtain on the basis of the virial the-
orem [81] f or the aver age kinetic energy of tra p ped ions
j
U ( R )
j
j
U ( R )
j
/2, and the velocity
D p 2. Next, because the parameters of a
forming ion are independent of the parameters of an incident ion, we have in the
region given in (6.42) P tr
D p 2
j
U ( R )
j
/ M ,whichgives v i / v tr
is v tr
D
p tr , and (6.43) gives for the number density of trapped
Search WWH ::




Custom Search