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Two-color excitation of highly charged ions with keV X-ray radiation:
a look from current experimental and theoretical RCE studies to XFEL perspectives
V.V.Balashov, A.A.Sokolik, A.V.Stysin
D.V.Skobeltsyn Institute of Nuclear Physics, M.V.Lomonosov Moscow State University, Moscow 119991, Russia
Parameters of X-ray radiation from RCE and XFEL devices in keV energy range
Channeled
423 MeV/u ions Fe24+
in [220] plane
of Si crystal [*,**]
The European XFEL
Technical Design Report
Wavelengths
Photon energy, keV
Coherence
Polarization
SASE 1
SASE 2
0.1 nm
12.4
yes
linear
0.1-0.4 nm
3.1 –1 2.4
yes
linear
SASE 3
0.4-1.6 nm
0.8 - 3.1
yes
circular, linear
0.07 – 0.46 nm
2.7 – 16.8
yes
circular, linear
[*] T.Azuma , Y.Takabayashi, C.Kondo, T.Muranaka et al.
PRL 97 (2006) 145502
[**] V.V.Balashov, A.A.Sokolik, V.K.Dolinov, A.V.Stysin,
JETP 107 (2008) 133; JETP Letters 89 (2009) 399.
X rays
< 100 >
The Okorokov resonance condition
ion
trajectory
θγ
< 001 >
q
channe
zion
er
l cent
1s2p : 1P1
< 010 >
6700.41 eV
1s2p : 3P1
~ 4.5 eV
X-ray
RCE
1s2 : 1S0
V.V.Balashov, A.A.Sokolik, A.V.Stysin, JETP 107 (2008) 133
Fe24+
φγ
< 100 >
X rays
ion
trajectory
θγ
< 001 >
q
channe
zion
er
l cent
1s2p : 1P1
< 010 >
6700.41 eV
1s2p : 3P1
X-ray
RCE
1s2 : 1S0
Fe24+
From spectral and geometrical properties of the resonating electric field
of the crystal to Stokes parameters of the characteristic X-ray radiation
The elliptic character of the resonating in-crystal
electric field in the rest frame of the trajectory
defined propagating ion under planar channeling
is the origin of variability of polarization properties
of the produced X-ray radiation.
But channeling is not a pre-requisite for resonant
coherent excitation !
1965 – 2006 : RCE exclusively with channeled ions –
V.V.Okorokov, Yad. Fiz. 2 (1965) 1009; Pis’ma Zh. Eksp. Teor.Fiz 2 (1965) 175
S.Datz, C.D.Moak et al., PRL 40 (1978) 843; NIM 170 (1980) 15
K.Komaki, T.Azuma et al., NIM B 146 (1998) 19,
and many other.
Since 2006:
RCE measurements with (a) channeled ions and (b) without channeling at all
Present-day portrait of the RCE process (the Okorokov effect) from Tokyo RCE measurements of 2006-2009:
Anisotropic X-ray emission from helium-like Fe24+ ions aligned by RCE with a periodic crystal potential –
T.Azuma et al., PRL 97 (2006) 145502;
Three-dimensional RCE of nonchanneling ions in a crystal –
C.Kondo et al., PRL 97 (2006) 135503;
Trajectory dependent RCE of planar-channeled ions in a thin Si crystal –
C.Kondo et al. NIM B 256 (2007) 157;
Doubly-resonant coherent excitation of HCI planar channeling in a Si crystal –
Y.Nakano et al., J.Phys. Conf.Series 58 (2007) 359;
Dressed atoms in flight through a periodic crystal field: X-UVU double resonances –
Y.Nakai et al., PRL 101 (2008) 113201;
RCE of lithium-like Li15+ ions in a thin Si crystal –
Y.Nakano et al., J.Phys. Conf.Series 163 (2009) 012094;
Polarization control in three-dimensional RCE –
Y.Nakano et al., PRL 102 (2009) 085502;
A unified concept for theoretical analysis of RCE data and suggestions
for new measurements (Moscow State University; 1998-2009)
Characteristic X-ray production in the RCE process
V.V. Balashov, I.V. Bodrenko -- Phys.Lett. A 352 (2006) 129
Metastable ion production in the RCE process
V.V. Balashov, I.V. Bodrenko -- NIM B 245 (2006) 52
Resonant coherent excitation of Ar17+ ions in planar channel of a silicon crystal
V.V. Balashov, A.A. Sokolik -- Optics and Spectroscopy 103 (2007) 761
Angular anisotropy of characteristic X-radiation and Auger electrons
during the resonance coherent excitation of relativistic ions under planar channeling
V.V.Balashov, A.A.Sokolik, A.V.Stysin -- JETP 107 (2008) 133.
Characteristic X-ray radiation and Auger electrons from resonant coherently
excited highly charged ions under channeling
V.V.Balashov, A.A.Sokolik, A.V.Stysin -- NIM B 267 (2009) 903.
Kinetics of double resonant coherent excitation of relativistic multicharged ions
in crystals beyond the channeling conditions
V.V.Balashov, A.A.Sokolik, A.V.Stysin -- JETP 108 (2009) 1010.
Angular anisotropy of the RCE X-rays under planar channeling as manifestation
of geometrical properties of the in-crystal electric field
V.V.Balashov, A.A.Sokolik, A.V.Stysin -- NIM B 267 (2009) 1772.
Polarization of photons emitted in the process of resonant coherent excitation
of relativistic ions under planar channeling
V.V.Balashov, V.K.Dolinov, A.A.Sokolik -- JETP Letters 89 (2009) 399.
Density matrix description of resonant coherent excitations of swift highly charged
ions in oriented crystals
V.V.Balashov, I.V.Bodrenko, V.K.Dolinov, A.A.Sokolik, A.V.Stysin –
J.Phys.Conf.Ser. 163 (2009) 012087.
Polarization and correlation aspects of resonant coherent excitation of fast highly charged
ions in crystals
V V Balashov -- J. Phys.: Conf. Ser. 212 (2010) 012028
2D RCE versus 3D RCE ?
Conceptually, 2D- and 3D- measurements complement each other in current RCE studies,
e.g.:
a)
exciting harmonic separation – clear advantage for 3D RCE; here, contrary to the 2D RCE case,
each resonating harmonic is characterized not only by its frequency ω klmbut also by its well defined
wave vector Kklm with |Kkl|m| not equal, generally, to ωklm;
a)
sensitivity to other, besides the oscillating electric field, intrinsic properties of the matter of ion
propagation, – clear advantage for 2D RCE; the profile and splitting of the resonances are here under
influence of the collective Lindhard potential of the crystal lattice (take an example of RCE of ionic
autoionizing states).
Common experimental difficulties and theoretical problems
in both cases of 2D RCE and 3D RCE studies:
a)
in the experiment – tuning to resonance harmonic;
b)
in the theory - unified description of both coherent and incoherent (relaxation)
ion-crystal interactions.
From single to double (two-color) resonant coherent excitation
Y.Nakano et al., J.Phys. Conf.Series 58 (2007) 359;
A remarkable variety of combinations of frequency ranges in double 2D or 3D resonant
coherent excitations – an important aspect in the parallel to be drawn between current
RCE and possible XFEL studies (see below).
From single to double (two-color) resonant coherent excitation
Y.Nakano et al., J.Phys. Conf.Series 58 (2007) 359;
A remarkable variety of combinations of frequency ranges in double 2D or 3D resonant
coherent excitations – an important aspect in the parallel to be drawn between current
RCE and possible XFEL studies (see below).
Conceptually, 2D- and 3D- measurements complement each other in current RCE studies,
e.g.:
a)
exciting harmonic separation – clear advantage for 3D RCE; here, contrary to the 2D RCE case,
each resonating harmonic is characterized not only by its frequency ω klmbut also by its well defined
wave vector Kklm with |Kkl|m| not equal, generally, to ωklm;
a)
sensitivity to other, besides the oscillating electric field, intrinsic properties of the matter of ion
propagation, – clear advantage for 2D RCE; the profile and splitting of the resonances are here under
influence of the collective Lindhard potential of the crystal lattice (take an example of RCE of ionic
autoionizing states).
Common experimental difficulties and theoretical problems
in both cases of 2D RCE and 3D RCE studies:
a)
in the experiment – tuning to resonance harmonic;
b)
in the theory - unified description of both coherent and incoherent (relaxation)
ion-crystal interactions.
Swift ion in matter is an open quantum system; key point of the
density-matrix RCE approach is in the unified time-dependent
description of both coherent and incoherent ion-crystal interactions
very small
for relativistic ions !
Ionization and spontaneous de-excitation probabilities (1013 s-1)
for Ar16+ and Fe 24+ ions in Si crystal in non-channeling condition
calculated at average target density 4.99 x 1022 cm –3.
1s2
2p2
1s2p
λionization
λionization
λX-ray
λionization
λX-ray
λAuger
Ar16+ (416 MeV/u)
13.6
28.3
10.5
52.2
12.4
34.5
Fe 24+ (433 MeV/u)
5.9
19.1
45.6
Swift ion in matter is an open quantum system; key point of the
density-matrix RCE approach is in the unified time-dependent
description of both coherent and incoherent ion-crystal interactions
General scheme of our
density-matrix approach
As soon as the in-crystal
electric field is known and
wave functions of the free
ion are chosen, one takes
standard quantum mechanics
to calculate matrix elements
Vpq(t) . The incoherence
parameters such as electron
loss and collision induced
level-to-level transition cross
sections are calculated or
taken from tables.
The equations are solved
numerically.Their solutions
are transformed into RCE
observables. When dealing
with those related to
polarization and angular
correlation RCE phenomena,
another aspect of the density
matrix technique – statistical
tensor calculations – is used
throughout.
Two-color excitation of highly charged ions with keV X-ray radiation:
a look from current experimental and theoretical RCE studies to XFEL perspectives
4.8 eV
to double RCE corrections from
2p -> 3s and 2p -> 3d excitations
n=3
3934-3936 eV
~ 0.6 keV
n=2
3318-3322 eV
~ 3.3 keV
n=1
Ar17
Exp,: Tokyo
Theory: Moscow
The combined frequencies in current two-color RCE studies
(n=1)→(n=2) and (n=2)→(n=3)
double RCE of hydrogen-like
ions
Combined
friequences
REFs
a) 3.3 keV;
b) 0.6 keV
C.Kondo et al., PRL 97 135503 (2006)
V.V.Balashov, A.A.Sokolik, A.V.Stysin,
JETP, 108 (2009) 1010
Auger electrons from double RCE
The same without channeling
Exp,: Tokyo
Theory: Moscow,
also strongly anisotropic angular distribution of
the Auger electrons predicted
The combined frequencies in current two-color RCE studies
Combined
friequences
REFs
(n=1)→(n=2) and (n=2)→(n=3)
double RCE of hydrogen-like
ions
a) 3.3 keV;
b) 0.6 keV
C.Kondo et al., PRL 97 135503 (2006)
V.V.Balashov, A.A.Sokolik, A.V.Stysin,
JETP, 108 (2009) 1010
RCE of autoionizing states in
helium-like ions; Ar16
a) 3.14 keV
b) 3.28 keV
Y.Nakano et al., J.Phys. Conf.Series 58
(2007) 359;
V.V.Balashov, A.A.Sokolik, A.V.Stysin
NIM B 267 (2009) 903.
Autler-Townes effect in resonant coherent
excitation of relativistic highly charged ions
in crystals
Autler-Townes doublet at resonant coherent excitation (RCE) of relativistic ions in crystals
without channeling
Ar 16+, 416 MeV/u
t (Si) ~ 1 μm
Tuning to coupling and probing resonances – by target rotation
Autler-Townes doublet at resonant coherent excitation (RCE) of relativistic ions in crystals
without channeling
Ar 16+, 416 MeV/u
t (Si) ~ 1 μm
Both coupling and probing
electric fields
in the ion rest frame
are strong!
Pprobing = 7.2 x 1015 W/cm2
Ppumpong = 2.8 x 1015 W/cm2
Survival fraction measurements
“Dressed atoms in flight through a periodic crystal
field” –Y.Nakai, Y.Nakano, T.Azuma et al. Phys.Rev.Lett. 101, 113201 (2008)
“Kinetics of double resonant coherent excitation of
relativistic multicharged ions in crystals beyond
channeling conditions” –
V.V.Balashov, A.A.Sokolik, A.V.Stysin JETP 108 (2009) 1010
Red lines –calculation
with 5x5 density matrix in basis
1s2:1S0; 1s2s:1S0; 1s2p:1P1(M=0;±1).
No fitting parameters.
Ω0 as a fitting parameter in the
Autler-Townes formula =
= 3.72 eV;
Ω0 as calculated matrix element
< 1s2p:1P1|V0,0,2|1s2s:1S0 >
of the field
= 3.55 eV
Autler-Townes
doublet in characteristic
X-ray
distribution
X-ray radiation
at double resonant coherent excitation
Arbitrary normalization
for experimental data
and results of the
calculations
Drastic change in both experiment and calculation [JETP
108 (2009) 1010] in profile of the Autler-Townes doublet
for X-ray photons detected in the (2,-2,0) plane direction
[horizontal] and perpendicular to this plane [vertical] -clear demonstration of the potential of the Autler-Townes
scheme in X-ray measurements to control polarization
characteristics of double excitation of highly charged ions.
Here - indication to “fine structure” magnetic quantum
number splitting of the Autler-Townes dublet
1s2s:!S0 -- 1s2p:!PM=0;±1.
The combined frequencies in current two-color RCE studies
Combined
friequences
REFs
(n=1)→(n=2) and (n=2)→(n=3)
double RCE of hydrogen-like
ions
a) 3.3 keV;
b) 0.6 keV
C.Kondo et al., PRL 97 135503 (2006)
V.V.Balashov, A.A.Sokolik, A.V.Stysin,
JETP, 108 (2009) 1010
RCE of autoionizing states in
helium-like ions; Ar16
a) 3.14 keV
b) 3.28 keV
Y.Nakano et al., J.Phys. Conf.Series 58
(2007) 359;
V.V.Balashov, A.A.Sokolik, A.V.Stysin
NIM B 267 (2009) 903.
Autler-Townes effect in double
RCE of helium-like ions; Ar16
a) 3.14 keV
b) 15.03 eV
Y.Nakai et al., PRL, 101, 113201 (2008)
V.V.Balashov, A.A.Sokolik, A.V.Stysin,
JETP, 108 (2009) 1010
Parameters of X-ray radiation from RCE and XFEL devices in keV energy range
Channeled
423 MeV/u ions Fe24+
in [220] plane
of Si crystal [*,**]
The European XFEL
Technical Design Report
Wavelengths
Photon energy, keV
Coherence
Polarization
SASE 1
SASE 2
0.1 nm
12.4
yes
linear
0.1-0.4 nm
3.1 –1 2.4
yes
linear
SASE 3
0.4-1.6 nm
0.8 - 3.1
yes
circular, linear
0.07 – 0.46 nm
2.7 – 16.8
yes
circular, linear
[*] T.Azuma , Y.Takabayashi, C.Kondo, T.Muranaka et al.
PRL 97 (2006) 145502
[**] V.V.Balashov, A.A.Sokolik, V.K.Dolinov, A.V.Stysin,
JETP 107 (2008) 133; JETP Letters 89 (2009) 399.
Also – high intensity of the photon energy flux: ~ 0.5 x 1016 W/cm2
(in the rest frame of propagating ion)
Conclusion
1. Made 45 years ago Okorokov’s prediction on resonant coherent excitation of fast ions in
crystals, famous S.Datz’s experiments united RCE with physics of highly charged ions and, now, the
breadth and irresistible appeal of current research in this area by the Tokyo RCE collaboration – all this
shows the process of resonant coherent excitation of fast highly charged ions in crystals as a real model for
future XFEL studies in the keV range. Its basic parameters in current experimental and theoretical works
(the produced photon energy, intensity of the X-ray radiation energy flux in the ion rest frame) look close
to those usually related to XFELs. Even of not less importance is the unique feature of RCE as a tunable
source of polarized X-ray radiation. True, RCE will never compete with lasers in whole. But the wide
experience gained in experimental and theoretical RCE studies, especially concerning polarization and
angular correlation aspects of the dynamics of various multi-photon processes in keV energy region, will be
a strong support among others for future XFEL experiments.
2. The variety of combinations of the frequency ranges between two partners in typical twocolor RCE processes – from almost equal to each other keV photons at two-step excitation of ionic
autoionizing states to the opposite strongly asymmetric case of soft, of some eV, pumping radiation
combined with probing X-ray radiation of several keV in the Autler-Townes RCE investigations – suggests
a real landmark for theoretical, experimental and, perhaps primarily, engineering work in preparing
concrete XFEL devices in the keV range.
3. On the other hand, a lot of studies must be done in the nearest future for further
development of the RCE methods themselves, as concerns their both fundamental aspects and possible
practical application.
Thank you!