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  

Channeled

The European XFEL 423 MeV/u ions Fe24+ Technical Design Report in [220] plane

of Si crystal [*,**]

SASE 1 SASE 2 SASE 3

Wavelengths 0.1 nm 0.1-0.4 nm 0.4-1.6 nm 0.07 – 0.46 nmPhoton energy, keV 12.4 3.1 –1 2.4 0.8 - 3.1 2.7 – 16.8Coherence yes yes yes yesPolarization linear linear circular, linear 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.

Parameters of X-ray radiation from RCE and XFEL devices in keV energy range

010

100

001

iontrajectory

ionz

channel center

010

100

001

iontrajectory

ionz

channel center

1s2 : 1S0

1s2p : 1P1

1s2p : 3P1

Fe24+

6700.41 eV

RCE X-ray

X rays

θγ

V.V.Balashov, A.A.Sokolik, A.V.Stysin, JETP 107 (2008) 133

The Okorokov resonance condition

~ 4.5 eV

010

100

001

iontrajectory

ionz

channel center

010

100

001

iontrajectory

ionz

channel center

1s2 : 1S0

1s2p : 1P1

1s2p : 3P1

Fe24+

6700.41 eV

RCE X-ray

X rays

θγ

φγ

The elliptic character of the resonating in-crystal electric field in the rest frame of the trajectory defined propagating ion under planar channelingis the origin of variability of polarization propertiesof the produced X-ray radiation.

From spectral and geometrical properties of the resonating electric field of the crystal to Stokes parameters of the characteristic 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) 175S.Datz, C.D.Moak et al., PRL 40 (1978) 843; NIM 170 (1980) 15K.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 processV.V. Balashov, I.V. Bodrenko -- Phys.Lett. A 352 (2006) 129

Metastable ion production in the RCE processV.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

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 ωklmbut 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 underinfluence 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.

2D RCE versus 3D RCE ?

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 ωklmbut 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 underinfluence 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.

very small for relativistic ions !

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

 

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

 

  1s2p

  2p2

 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

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 – statisticaltensor calculations – is used throughout.

General scheme of ourdensity-matrix approach

4.8 eV

Two-color excitation of highly charged ions with keV X-ray radiation:a look from current experimental and theoretical RCE studies to XFEL perspectives 

to double RCE corrections from 2p -> 3s and 2p -> 3d excitations

Exp,: Tokyo

Theory: Moscow

Совмещение двух характерных приемов последнего времени для наблюдения эффекта Окорокова : а) RCE без каналирования; б) “two-colour” excitation.

3318-3322 eV

3934-3936 eV

n=2

n=3

n=1

Ar17

~ 0.6 keV

~ 3.3 keV

 

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

     

 

 

   

Auger electrons from double RCE

The same without channeling

Exp,: TokyoTheory: 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 keVb) 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 ionsin 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

Pprobing = 7.2 x 1015 W/cm2 Ppumpong = 2.8 x 1015 W/cm2

Both coupling and probing electric fields

in the ion rest frame are strong!

Survival fraction measurements

“Dressed atoms in flight through a periodic crystalfield” –Y.Nakai, Y.Nakano, T.Azuma et al. -Phys.Rev.Lett. 101, 113201 (2008)

“Kinetics of double resonant coherent excitation ofrelativistic multicharged ions in crystals beyondchanneling 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

X-ray distribution

Arbitrary normalizationfor experimental dataand 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 dublet1s2s:!S0 -- 1s2p:!PM=0;±1.

Autler-Townes doublet in characteristicX-ray radiation

at double resonant coherent excitation

 

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 keVb) 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

Channeled

The European XFEL 423 MeV/u ions Fe24+ Technical Design Report in [220] plane

of Si crystal [*,**]

SASE 1 SASE 2 SASE 3

Wavelengths 0.1 nm 0.1-0.4 nm 0.4-1.6 nm 0.07 – 0.46 nmPhoton energy, keV 12.4 3.1 –1 2.4 0.8 - 3.1 2.7 – 16.8Coherence yes yes yes yesPolarization linear linear circular, linear 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.

Parameters of X-ray radiation from RCE and XFEL devices in keV energy range

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 thisshows 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 two-color 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!