Sensitivity to Secondary Electron Emission Charging Processes
Charging Time to Reach Equilibrium Surface Potential
Charging Studies: 4 specific Cases
As described in the previous section on charging processes, dust grains in space are charged by the competing effects of electron and ion capture from the ambient plasma, secondary electron emission from the impacts of high energetic ions or electrons, on the release of photoelectrons from the ambient UV radiation field and on the relative velocity of between the plasma and the grain. Thermionic and field emission effects are negligible for Quiet conditions in the Earth's magnetosphere, but are not negligible when dust potentials are charged negatively to thousands of volts.
For our simulations, we implemented the same charging processes a those used by Horányi, Juhász and their coworkers,, with the exception of two: secondary electron emission by back-scattered electrons, and secondary electron emission by proton impact. For the Earth's magnetosphere and Quiet plasma conditions, those extra secondary electron emission processes add a few volts positive to the potentials that we calculate using electron/ion capture from the ambient plasma, secondary electron emission from ion impact, and photoelectron emission from the ambient UV radiation field [private comm. with Juhász, February/March 2000]. For the Earth's magnetosphere and Active plasma conditions, those extra secondary electron emission processes are a small effect compared to the unknowns of the plasma conditions and the material properties. The charging currents are poised in a delicate balance, and therefore, small changes in the plasma parameters can have large effects on the particles' charges.
Equilibrium dust potential is reached when the sum of all of the charging currents is zero. The dominant electron capture from plasma leads to negative charges. Secondary and photoelectron emission charging processes are highly material dependent, therefore, in the high-energy region of geosynchronous orbit and the plasma sheet, the plasma particles may be charged positively or negatively.
Equilibrium Potential from Juhász and Horányi
Juhász and Horányi [25] find the following equilibrium potentials
for Quiet plasma conditions for a dielectric grain (material properties
= 2.4, Em = 400 eV, 
=0.1) in
the Earth's magnetosphere.
Figure 18: Equilibrium potentials for a spherical grain in Earth's magnetosphere under Quiet plasma conditions [25]. Inside of the plasmasphere, the grains charge negatively due to negligible secondary electron emission. The grains most negatively charged are in the region of the Earth's shadow, where photoelectron production currents are zero. Outside of the plasmasphere, the grain equilibrium potentials are positive due to dominating secondary electron emission.
The time to acquire the equilibrium charge may be longer than the flight trajectory time of the particle, therefore, we must consider the charging times for different regions and different particle sizes in Earth's magnetosphere, for both Quiet and Active plasma conditions. The charging time generally increases with decreasing particle radii a.
We can calculate a rough estimate of the charging time using the following expression. The charging time by electron capture from a plasma in local thermal equilibrium is [33] (using now the variable s for particle radius):
s cm-3 cm;
Equation 16
In our equilibrium potential calculations, we calculate the charging time as:
Charging time = (-1.* time_eps
* delta_time) / ln(eps);
Equation
17
where: time_eps = the time for a particle's potential to reach an equilibrium
(e.g. the present potential does not change from the previous value by more than a minuscule amount: eps).
eps = the accuracy reached for unchanging potentials
delta_time = the time increments for each potential calculation
If we plot the potential values, they reach a nonchanging value, an example is the next figure.
Figure 19: An example of the equilibrium potential calculation.
If we apply the rough plasma values from Table 5, then we arrive at the following overview of dust potentials and charging times.
Figure 20: Dust potentials in different regimes of the Earth's magnetosphere using rough plasma parameters.
Figure 21: The charging times of a 1 micron-sized-particle in the different plasma regimes. We consider dust potentials from Fig. 20 and LTE plasma parameters [Table 5].
Charging Studies: 4 specific Cases
In order to learn more about the equilibrium potentials and the relevant currents
for particles of different material properties, we performed a study of charging a 1 micron spherical dust particle
in a two-component plasma, similar to the plasma at geosynchronous distance. The cold plasma component has an energy
of 300 eV, and the hot component has an energy > 1 keV. Two types of plasma conditions were considered: Quiet
conditions when the cold plasma prevails, and "disturbed" ("Active") plasma conditions, when
the hot plasma prevails. We considered several different secondary electron emission coefficients
and peak energies Em and two types of photoelectron yields
.
Case 1
Case 2
Case 3
Case 4
= 1.5
= 2.4
= 1.4
= 1.5
Em = 250 eV
Em = 400 eV
Em = 180 eV
Em = 250 eV
=0.1 =0.1 =0.1 =1.0
Quiet plasma conditions
Disturbed plasma conditions
Disturbed plasma conditions
Quiet plasma conditions
Table 6: Parameters used for charging study.
We calculated as a function of the dust potential the different charging
currents: electron and ion collection currents, secondary electron emission currents, for both cold and hot components,
and the photoelectron current. From the total current we determined the equilibrium potential. The mean energy
of the photoelectrons is assumed to be 2 eV, and that of the secondary electrons is assumed to be 2.5 eV.
Since the region of geostationary orbit at 6.6RE is an interesting region for satellite operators, we follow this section with a look at some charging processes for dust particles in GEO, and we compare the results to a region in space further out at 16 RE. The following figures show our results for this charging study.
Case 1
Figure 22: The top graph shows equilibrium potential and charging from
Quiet plasma conditions and dust material properties
= 1.5, Em = 250 eV, =0.1.
The resulting equilibrium potential is Uequ = +4.5 V. Because of the dominating secondary electron
current from the low energy, the equilibrium potential is a few Volts positive. The lower two panels show the equilibrium
potential in Volts and the charging time in seconds in the Earth's magnetosphere from 3 RE to 14 RE,
and 360 degree local time in units of 0 to 24 hours (12 L.T. points towards the Sun and 0 L.T. is in the Earth's
shadow. The local time 18 hours is in the teardrop portion of the Earth's magnetotail (see Figure 18)).
Case 4
Case 4 has the same material properties as Case 1, except for the photoelectron
yield is 10 times higher. This case
has the canonical material properties for a conducting particle which Horányi, Juhász and their co-workers
[14,
23,
24,
25,
26] use in their studies. We place this case here for easier comparison with Case 1.
Figure 23: Equilibrium potential in Volts and charging times in seconds
in the Earth's magnetosphere under Quiet plasma conditions for a 1 micron spherical dust particle with material
property parameters = 1.5, Em
= 250 eV, =1.0.
Case 2
Figure 24: The top graph shows equilibrium potential and charging from
Active plasma conditions and dust material properties
= 2.4, Em = 400 eV, =0.1.
The resulting equilibrium potential is Uequ = +3.1 V. Because of the dominating secondary electron
current for this high yield material, the equilibrium potential is a few Volts positive. The lower two panels show
the equilibrium potential in Volts and the charging time in seconds in the Earth's magnetosphere from 3 RE
to 14 RE, and 360 degree local time in units of 0 to 24 hours (12 L.T. points towards the Sun and 0
L.T. is in the Earth's shadow. The local time 18 hours is in the teardrop portion of the Earth's magnetotail (see
Figure 18).).
Case 3
Figure 25: The top graph shows equilibrium potential and charging from
Active plasma conditions and dust material properties
= 1.4, Em = 180 eV, =0.1
The resulting equilibrium potential is Uequ = -3039.2 V. The dominant flux is from the collection
of the high-energy electrons. For this low yield material, the equilibium potential is highly negative. The lower
four panels show the equilibrium potential in Volts and the charging time in seconds in the Earth's magnetosphere
from 3RE to 8 RE, and from 9 RE to 14 RE and 360 degree local time
in units of 0 to 24 hours (12 L.T. points towards the Sun and 0 L.T. is in the Earth's shadow. The local time 18
hours is in the teardrop portion of the Earth's magnetotail (see Figure 18)).
Now we examine the charging processes on a 1 micron-sized particle at geostationary orbit (6.6 RE).
Quiet conditions, Conducting 1 micron-sized particle
Figure 26: The canonical case for a conducting 1 micron-sized spherical
dust particle to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties
are
= 1.5, Em = 250 eV, =1.0, and the plasma conditions are Quiet. The graphs
show, from top to bottom: equilibrium potentialand charging currents versus 360 degree local time in units of 0
to 24 hours. The equilibrium potential ranges from +2V to +9V, the charging time ranges from a few seconds to a
minute, and the dominant current is the electron collection current.
Disturbed ("Active") conditions, Conducting 1 micron-sized particle
Figure 27: The canonical case for a conducting 1-micron sized spherical
dust particle to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties
are
= 1.5, Em = 250 eV, =1.0, and the plasma conditions are Active ("disturbed").
The graphs show, from top to bottom: equilibrium potential, and charging currents versus 360 degree local time
in units of 0 to 24 hours. The equilibrium potential ranges from +2V to +4V, the charging time ranges from about
3 to 10 seconds, and the dominant current is the electron collection current.
Quiet conditions, Dielectric 1 micron-sized particle
Figure 28: The canonical case for a dielectric 1 micron-size spherical
dust particle to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties
are
= 2.4, Em = 400 eV, =0.1, and the plasma conditions are Quiet. The graphs
show, from top to bottom: equilibrium potential and charging currents versus 360 degree local time in units of
0 to 24 hours. The equilibrium potential ranges from + 0V to +6V, the charging time from about 10 seconds to a
minute-and-a-half, and the dominant current is the electron collection current.
Disturbed ("Active") conditions, Dielectric 1 micron-sized particle
Figure 29: The canonical case for a dielectric spherical dust particle
to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties are
= 2.4, Em = 400 eV, =0.1, and the plasma conditions are Active ("disturbed").
The graphs show, from top to bottom: equilibrium potential and charging currents versus 360 degree local time in
units of 0 to 24 hours. The equilibrium potential ranges from +3V to +4V, the charging time from about 5 to 10
seconds, and the dominant current is the electron collection current.
Here we list a summary from Figures 26-29 of the top two charging processes for the equilibrium potentials of a 1 micron-sized particle in geostationary orbit, for specific local time (L.T.) locations. (12 L.T. points towards the Sun and 0 L.T. is in the Earth's shadow. The local time 18 hours is in the teardrop portion of the Earth's magnetotail (see Figure 18).).
| Particle Type | Plasma Condition | 6 L.T. | 12 L.T. | 18 L.T. | 20 L.T. | 24 L.T. |
| Conducting | Quiet | ec, pec | ec, pec | ec, pec | ec, pec | ec, pec |
| Conducing | Disturbed | ec, sec | ec, sec | ec, sec | ec, sec | ec, pec/sec |
| Dielectric | Quiet | ec, pec | ec, sec | ec, sec | ec, sec | ec, pec |
| Dielectric | Disturbed | ec, sec | ec, sec | ec, sec | ec, sec | ec, sec |
ec = electron collection current
pec = photoelectron current
sec = secondary electron current
Table 7: Dominant charging processes for a 1 micron-sized particle in
geostationary orbit.
Next, we list sample numbers from the above data for charging times and equilibrium potentials for a conducting 1 micron-sized particle in Active ("disturbed") and Quiet plasma conditions in GEO, for specific local time (L.T.) locations. Note that typical charging times are 10 times faster under Active plasma conditions, due likely to the more higher flux of electrons onto the particle.
Material properties and currents are the following.
- secondary electron emission parameters: delsec=1.5, emaxsec=250 eV
- photoelectron emission chi = 1.0
- Maxwellian temperature distribution for photoelectron emission tp=2.0 eV
- conducting particle
- Currents: ion/electron collection, photoemission, secondary electron emission- electron impact
QUIET PLASMA: Type 1 (conducting), in Geostationary orbit
| Size (micron) | Local Time | Charging Time (sec) | Equil Potential (V) |
| 1000 | 0 | .05 | 5.5 |
| 100 | 0 | .2 | 5.5 |
| 10 | 0 | 1.5 | 5.5 |
| 1 | 0 | 12.3 | 5.5 |
| 1000 | 3 | .07 | 4.9 |
| 100 | 3 | .2 | 4.9 |
| 10 | 3 | 1.2 | 4.9 |
| 1 | 3 | 10.0 | 4.9 |
| 1000 | 6 | .05 | 5.6 |
| 100 | 6 | .2 | 5.6 |
| 10 | 6 | 1.6 | 5.6 |
| 1 | 6 | 13.1 | 5.6 |
| 1000 | 9 | .07 | 6.4 |
| 100 | 9 | .3 | 6.4 |
| 10 | 9 | 2.3 | 6.4 |
| 1 | 9 | 18.4 | 6.4 |
| 1000 | 12 | .09 | 6.7 |
| 100 | 12 | .3 | 6.7 |
| 10 | 12 | 2.7 | 6.7 |
| 1 | 12 | 21.8 | 6.7 |
| 1000 | 15 | .09 | 7.1 |
| 100 | 15 | .4 | 7.1 |
| 10 | 15 | 3.7 | 7.1 |
| 1 | 15 | 29.2 | 7.1 |
| 1000 | 18 | .1 | 8.7 |
| 100 | 18 | .9 | 8.7 |
| 10 | 18 | 7.4 | 8.7 |
| 1 | 18 | 56.6 | 8.7 |
| 1000 | 21 | .005 | 2.0 |
| 100 | 21 | .05 | 2.0 |
| 10 | 21 | .3 | 2.0 |
| 1 | 21 | 2.2 | 2.0 |
ACTIVE PLASMA: Type 1 (conducting), in Geostationary orbit
| Size (micron) | Local Time | Charging Time (sec) | Equil Potential (V) |
| 1000 | 0 | .007 | 2.5 |
| 100 | 0 | .06 | 2.5 |
| 10 | 0 | .4 | 2.5 |
| 1 | 0 | 3.4 | 2.5 |
| 1000 | 3 | .006 | 2.3 |
| 100 | 3 | .06 | 2.3 |
| 10 | 3 | 0.4 | 2.3 |
| 1 | 3 | 3.4 | 2.3 |
| 1000 | 6 | .006 | 2.6 |
| 100 | 6 | .06 | 2.6 |
| 10 | 6 | .4 | 2.6 |
| 1 | 6 | 3.3 | 2.6 |
| 1000 | 9 | .006 | 2.9 |
| 100 | 9 | .06 | 2.9 |
| 10 | 9 | .4 | 2.9 |
| 1 | 9 | 3.4 | 2.9 |
| 1000 | 12 | .007 | 3.2 |
| 100 | 12 | .07 | 3.2 |
| 10 | 12 | .5 | 3.2 |
| 1 | 12 | 4.0 | 3.2 |
| 1000 | 15 | .009 | 3.8 |
| 100 | 15 | .09 | 3.8 |
| 10 | 15 | .7 | 3.8 |
| 1 | 15 | 5.6 | 3.8 |
| 1000 | 18 | .01 | 4.1 |
| 100 | 18 | .1 | 4.1 |
| 10 | 18 | .7 | 4.1 |
| 1 | 18 | 6.3 | 4.1 |
| 1000 | 21 | .007 | 3.0 |
| 100 | 21 | .07 | 3.0 |
| 10 | 21 | .5 | 3.0 |
| 1 | 21 | 4.2 | 3.0 |
Table 8. Some charging times and equilibrium potentials for a conducting 1 micron-sized particle in Active ("disturbed") and Quiet plasma conditions in GEO (12 L.T. points towards the Sun and 0 L.T. is in the Earth's shadow. The local time 18 hours is in the teardrop portion of the Earth's magnetotail (see Figure 18).
In the outer magnetospheric region near the solar wind at 16 RE, the plasma conditions are the same for both disturbed (Active) and Quiet conditions, therefore, we don't distinguish between those two plasma conditions in the following work.
Conducting 1 micron-sized particle
Figure 31 The canonical case for a conducting 1 micron-sized spherical
dust particle to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties
are
= 1.5, Em = 250 eV, =1.0. The graphs show, from top to bottom: equilibrium
potential and charging currents versus 360 degree local time in units of 0 to 24 hours, with the lowest graph an
expansion of the upper one, in order to see better the charging currents. The equilibrium potential ranges from
+6V to +11V, and the dominant current is the electron collection current.
Dielectric 1 micron-sized particle
Figure 32: The canonical case for a dielectric spherical dust particle
to compare with Horányi, Juhász and their co-workers [14,
23,
24,
25,
26]. The material properties are
= 2.4, Em = 400 eV, =0.1. The graphs show, from top to bottom: equilibrium potential
and charging currents versus 360 degree local time in units of 0 to 24 hours, with the lowest graph an expansion
of the graph above it, in order to see better the charging currents. The equilibrium potential ranges from 6 to
11V, and the dominant current is the electron collection current.
Next, we list a summary from Figures 31-32 of the top two charging processes for the equilibrium potentials in the outer portion, at 16 RE, of the Earth's magnetosphere, for specific local time (L.T.) locations. (12 L.T. points towards the Sun and 0 L.T. is in the Earth's shadow. The local time 18 hours is in the teardrop portion of the Earth's magnetotail.).
| Particle Type | 6 L.T. | 12 L.T. | 18 L.T. | 20 L.T. | 24 L.T. |
| Conducting | ec, sec | ec, pec | ec, sec | ec, pec | ec, sec |
| Dielectric | ec, pec | ec, sec | ec, sec | ec, sec | ec, sec |
ec = electron collection current
pec = photoelectron current
sec = secondary electron current
Table 9: Top two charging processes for a conducting 1 micron-sized particle in the outer portion of the Earth's magnetosphere at 16 RE.
Go to:
Dust Charging Results
|
|
|