150
M. F. Ciappina et al.
approaching to 10
19 W/cm
2 are being routinely used in many laser facilities. Furthermore, several lasers of petawatt (PW) power [1] could deliver pulses of intensities
on the order of 10
22 W/cm
2 , depending on the size of the focal region. Singular
reports of even higher intensities 10
22 W/cm
2 [2–4] are still lacking independent
and unambiguous evidences. However, the forthcoming commissioning of several
new 10-PW class laser facilities [5–10] opens a way to a new considerable step
forward. For a laser power of 3 PW, expected to be reached at the ELI-Beamlines
facility within the next 2–3 years, the peak intensity in a 3λ focal spot of an 800-nm
laser pulse will exceed 5 × 10
22 W/cm
2 . With 10 PW laser pulses focused down to
the diffraction limit, intensities on the order of 10
24 W/cm
2 or even higher can be
achieved.
This experimental breakthrough is expected to make novel regimes of laser-matter
interactions accessible for research including: the radiation-dominated regime, where
radiation friction forces play the major role in plasma dynamics; observation and
quantification of relativistic tunneling; generation of QED cascades of elementary
particles developed from seed particles in a laser focus and a large zoo of other effects
inaccessible at presently available laser intensities. For the overview of this newly
emerging research area we direct the reader to reviews [11–13] and the literature
quoted there.
In view of these prospects, the problem of precise and univocal determination of
the electromagnetic field intensity in a laser focus becomes of singular importance.
Here we propose using tunneling ionization of multicharged ions as a probe of laser
intensity. The main advantage of this approach has its root in the highly nonlinear dependence of the tunneling ionization probability on the electromagnetic field
strength, so that a relatively small change in intensity leads to orders of magnitude
variation in the ionization rate. As a consequence, the maximal ionic charge observed
in a laser focus becomes a highly sensitive function of the peak intensity. The shape
of photoelectron spectra and positions of the spectral maximum in a circularly polarized field [14] and the high-energy cut-off in a linearly polarized field [15] are also
sensitive to the value of intensity and have been extensively employed for its determination. In general, at moderate intensities I ≤ 10
15 W/cm
2 , when single-electron
ionization remains the dominant process, photoelectron spectra are the most efficient and reliable tool to measure the laser intensity [16, 17]. With its value growing,
multiple ionization comes into play along with two competing mechanisms known
as sequential and nonsequential ionization, with the latter triggered by the so-called
recollisions [18–21]. Recollision takes place when the laser-ionized electron returns
close to the ion core, driven by the laser electric field, that has now reversed its direction. In this re-encounter, this recolliding electron can elastically rescatter with the
ion or trigger the above two mentioned processes. Interplay of the two mechanisms
makes the interval I 10
15 –10
17 W/cm
2 difficult for unambiguous determination
of intensity via the ionization process. A further increase of intensity simplifies the
situation again. As soon as the electron motion after the ionization step becomes
relativistic which, for λ = 800 nm happens at I ≈ 10
17 W/cm
2 , the longitudinal
photoelectron drift induced by the Lorentz force makes the recollision with the ion
core impossible, so that the sequential tunnel ionization remains the only relevant
M. F. Ciappina et al.
approaching to 10
19 W/cm
2 are being routinely used in many laser facilities. Furthermore, several lasers of petawatt (PW) power [1] could deliver pulses of intensities
on the order of 10
22 W/cm
2 , depending on the size of the focal region. Singular
reports of even higher intensities 10
22 W/cm
2 [2–4] are still lacking independent
and unambiguous evidences. However, the forthcoming commissioning of several
new 10-PW class laser facilities [5–10] opens a way to a new considerable step
forward. For a laser power of 3 PW, expected to be reached at the ELI-Beamlines
facility within the next 2–3 years, the peak intensity in a 3λ focal spot of an 800-nm
laser pulse will exceed 5 × 10
22 W/cm
2 . With 10 PW laser pulses focused down to
the diffraction limit, intensities on the order of 10
24 W/cm
2 or even higher can be
achieved.
This experimental breakthrough is expected to make novel regimes of laser-matter
interactions accessible for research including: the radiation-dominated regime, where
radiation friction forces play the major role in plasma dynamics; observation and
quantification of relativistic tunneling; generation of QED cascades of elementary
particles developed from seed particles in a laser focus and a large zoo of other effects
inaccessible at presently available laser intensities. For the overview of this newly
emerging research area we direct the reader to reviews [11–13] and the literature
quoted there.
In view of these prospects, the problem of precise and univocal determination of
the electromagnetic field intensity in a laser focus becomes of singular importance.
Here we propose using tunneling ionization of multicharged ions as a probe of laser
intensity. The main advantage of this approach has its root in the highly nonlinear dependence of the tunneling ionization probability on the electromagnetic field
strength, so that a relatively small change in intensity leads to orders of magnitude
variation in the ionization rate. As a consequence, the maximal ionic charge observed
in a laser focus becomes a highly sensitive function of the peak intensity. The shape
of photoelectron spectra and positions of the spectral maximum in a circularly polarized field [14] and the high-energy cut-off in a linearly polarized field [15] are also
sensitive to the value of intensity and have been extensively employed for its determination. In general, at moderate intensities I ≤ 10
15 W/cm
2 , when single-electron
ionization remains the dominant process, photoelectron spectra are the most efficient and reliable tool to measure the laser intensity [16, 17]. With its value growing,
multiple ionization comes into play along with two competing mechanisms known
as sequential and nonsequential ionization, with the latter triggered by the so-called
recollisions [18–21]. Recollision takes place when the laser-ionized electron returns
close to the ion core, driven by the laser electric field, that has now reversed its direction. In this re-encounter, this recolliding electron can elastically rescatter with the
ion or trigger the above two mentioned processes. Interplay of the two mechanisms
makes the interval I 10
15 –10
17 W/cm
2 difficult for unambiguous determination
of intensity via the ionization process. A further increase of intensity simplifies the
situation again. As soon as the electron motion after the ionization step becomes
relativistic which, for λ = 800 nm happens at I ≈ 10
17 W/cm
2 , the longitudinal
photoelectron drift induced by the Lorentz force makes the recollision with the ion
core impossible, so that the sequential tunnel ionization remains the only relevant