Ionisation Coe ffi cient ( β )

During the meteor ablation process, a certain fraction of the kinetic energy loss is used for ionisation production. This fraction is τq, the ionisation efficiency, which relates to β. For β >1, secondary ionisation occurs with a per-collision ionisation probability ofβ0. The relation

betweenτqandβis given below, whereΦqis the average ionisation energy:

τq =

2Φq

µv2β (3.12)

Because the ionisation energy of molecular nitrogen (the dominant atmospheric constituent at meteor heights, ∼ 15 eV) is greater than the ionisation energy of typical meteoric atoms (∼ 8 eV), we expect meteoric atoms to be preferentially ionised, at least for slower meteor speeds. This implies that the electrons produced in the trail are mainly derived from meteoric atoms.

inaccuracies. In their work, the total ionisation coefficient is less than the primary ionisation probability for speeds less than∼48 km/s, which is unphysical. Furthermore, their expression forβgives a non-zero probability of ionisation for collisions involving less kinetic energy than is required for ionisation to occur.

Jones (1997) has performed the most detailed modern review of estimating β based on theory and observation. He derived an expression for the primary ionisation probability (β0) in

terms of the relevant scattering cross sections:

β0 = σion σela+σion = c(v−v0)2v0.8 1+c(v−v0)2v0.8 (3.13)

The minimum speed at which ionisation can occur isv0. For speeds less than this, a mete-

oric atom does not possess enough kinetic energy to become ionised during a collision with an air molecule. As defined,β0 must be valued between zero and unity, since primary ionisation

can occur only once. In the above equation,σion represents the ionisation cross section, which

is assumed to be proportional to (v−v0)2(Sida, 1969). The elastic scattering cross section,σela,

is assumed to be proportional tov−0.8 (Bronshten, 1983), and is added to σion to approximate

the total collisional cross section. The constantc is a scaling coefficient, which Jones (1997) computed so that σion agreed with Bronshten (1983) at 40 km/s. Jones (1997) lists values of v0 andc for atomic oxygen, iron, copper, magnesium, and silicon. We list his values (except

copper) in Table 3.1.

At higher collision energies, the probability of secondary ionisation increases, leading to β > β0. As an example, the first two ionisation energies for oxygen are 13.6 and 35.1 eV.

This means that an oxygen atom would require a minimum speed of about 30 km/s before having a significant probability of becoming ionised a second time. Jones (1997) introduced a “correction” term to Eq. 3.13 to giveβin terms ofβ0:

β(v)= β0+2 Z v v0 dv0β0(v 0 ) v0 (3.14)

In performing this analysis, the assumed elemental composition greatly affects the result, as β is determined from the ionisation probabilities of the constituent elements, weighted by the proportion of the number of atoms present. Fig. 3.1 shows β computed according to Jones’ (1997) method for CI-Carbonaceous Chondrites, H-Ordinary Chondrites, and Iron- Nickel compositions, to emphasise the effect of compositional differences. The CI chondritic composition best represents the composition of cometary meteoroids (Boroviˇcka, 2006), while the H chondritic and iron-nickel compositions represent asteroidal and pure iron compositions, respectively. Only the elements oxygen, iron, magnesium, and silicon were used, as these four elements represent the majority for each composition type (Lodders and Fegley, 1998). The weight percentage of each element for each composition are given in Table 3.1. However, we rescaled these to account for the remaining weight percentage not covered by our assumed compositions. This may introduce a small error, but eliminates the need to defineβ0as a lower

limit.

We note however, that these four elements have higher ionisation energies. At low speed, Na, Al, and Ca may contribute significantly to the number of free electrons. Because of this, ourβmay not be valid for the slowest meteors.

As shown in Fig. 3.1, the iron-nickel β is an order of magnitude larger than β for the CI/H chondritic compositions. As the first ionisation energy of oxygen is about twice that for iron, a composition dominated by oxygen is expected to have lower β. We use the H- Chondritic composition for our data since it is similar to CI-Chondritic, and therefore a good average fit for both cometary and most asteroidal meteoroids. This means we do not require orbital information to determine the class of the assumed parent body composition, as nearly pure iron meteoroids compose ∼10% of all meteoroids at our sizes (Boroviˇcka et al., 2005).

Figure 3.1: Total ionisation coefficient for CI-Carbonaceous and H-Ordinary chondritic, and Iron Nickel type meteoroids. The Fe-Ni behaviour shows an order of magnitude difference, emphasising the importance of compositional differences.

Assuming our meteors to be H-Chondritic impliesµ = 0.0241 kg/mol, and that our rescaling of the weight percentages for the missing 5.9% is not significant. Ourβ can be approximated (withvin units of km/s) as:

log₁₀β= 5.84−0.09v0.5−9.56/log₁₀v (3.15) Thisβis closely proportional to v4.0_{between 20 and 40 km}/_{s. The speed exponent of this}

approximate proportionality decreases with increasing meteor speed.