ABSTRACT
As the magnitude of vector composed by two circularly-polarized hefts holds the line in an optical cycle, the ionization rate in the static field can be substituted for that in alternating when laser field is circularly-polarized [1,6]:
(4.b)
We can discover based on the induction and analysis that the formula of tunneling ionization rate of atoms and ions in a linearly polarized laser field which has been widely discussed and applied in reference [6] is described as follows by mistake.t8, ^
(5)
Now we discuss the effect on the calculation of threshold laser intensity on account of the error in formula (5). The threshold laser intensity can be estimated with ID quasiclassical coulomb Barrier-Suppression Ionization (BSI) model by Augst[10]
(6) Table 1 Calculated threshold laser intensities for Xe I to Xe VIII using the formula (4) and (5) when the ionization rate is 1012s_I
Ions of Xe IE(eV)
li (W/cm2) I2(W/cm2) 02-II)/Il
Xe,+
12.127 4.79E13 5.49E13 14.54 %
Xe2+
Xe3+
32.1 3.55E14 3.89E14 9.49 %
Xe4+
45.5 8.30E14 9.01E14 8.62 %
Xe5+
Xe6+
68.0 1.96E15 2.10E15 7.29 %
Xe7+
96.0 5.53E15 5.93E15 7.28 %
Xe8+
110.0 7.44E15 7.95E15 6.90 %
Table 1 shows that the laser threshold intensities Ii ^ I2 are needed to produce Xe atom's eight charge ions when the ionization rate calculated by formula (4) and (5) is 1012s_1. The error [(I2 - Ii) / Ii]is greater than 10% for Xe I and Xe II due to the mistake in
12„-1 formula (5) when the ionization rate is about 10 s" in table 1, and that the error[(l2 - Ii) / Ii] is less than 10% for more than two charge ions. When the ionization rate is 1014s_1, the errors are about 23.06 %, 10.08 % and 8.54 % respectively for each> five and eight charge ions due to the mistake in formula(5). Thus the calculated results have been
affected for low charge ions because of the error when the ionization rate and threshold laser intensities are calculated in some references which cite the formula (5), and the impact on high charge ions is small due to the small errors. The depending relationship between the ionization rate of Kr I to Kr IX in a circularly polarized laser field and laser intensity is calculated according to formula4.b.The ADK-model-calculated ionization rate of Kr I to Kr IX as the
function of laser intensity is presented for laser pulse width Tp=105fs in Fig.l. The establishment of electron energy distribution model is simplified as follows: 1) In the low electron density(<1019cm"3), the time of laser pulse duration(usual tens of femtoseconds ~ 500 femtoseconds) is shorter than that of collision between electrons (>lps)[11], the plasma heating caused by collision between electrons is neglected in the calculation of electron energy distribution; 2) The inverse bremsstrahlung absorption originated from the collision between electrons and ions is neglected; 3) The ionization rate can be calculated with ADK model because that depends little on the laser
Fig.l Calculated ionization rate of Kr I to Kr IX as the function of laser intensity
The ratio of formula (4.a) and formula (5) is about 2.60 .
