Article on X-ray optics, capillary optics, capillary lens, nanotechnology, photon crystals, quantum crystals

Article on x-ray capillary optics

INTRODUCTION

             Approximately twenty five years after the discovery of the X-ray by

Professor W. Roentgen,   Compton revealed: X-rays were possible to reflect from smooth surfaces, for example, from glass. The latter discovery was used in 1931 by F. Jentzch and E. Nahring, who carried out the experiment on transmission of X-radiation through a glass capillary¹.

             The most well-known experiment after World War II was the one carried out by R.V. Pound and G.A. Rebke at the Harvard University², They used a glass tube several meters long for analysis of a resonance radiation of Fe⁵⁷ nucleus (E=14,4 keV).

In the beginning of the 1980s the investigations on transmission of X-ray through glass monocapillaries and on focusing the synchrotron radiation were performed at the Kurchatov Atomic Energy Institute (Moscow, Russia), in the laboratory of Professor M. Kumakhov^3-5.

             P. Engstrom, S.Larsson, A. Rindby and B.Stocklassa performed first experiments on X-ray fluorescence [XRF], using tapered monocapillaries for increasing the density of X-ray beams⁶. Focusing the synchrotron radiation by means of the tapered monocapillaries was carried out by groups of D.N. Bilderback⁷ and D.A. Carpenter⁸.



Kumakhov Optics

         In the early 1980s, M. Kumakhov revealed the new way of controlling fluxes of the neutral particles – X-ray and neutron radiation^9-10.

         First X-ray optical and neutron optical systems that adapted the new method and technology were created and tested in the laboratory of Prof. Kumakhov.

The optics, later, obtained its name “KUMAKHOV OPTICS”. The instrument based on this method was named “KUMAKHOV LENS”. In scientific publications the optics is, at the same time, entitled “polycapillary optics”.

         Polycapillary optics, actually, is only a part of Kumakhov optics.

                Several general figures can be presented to reveal the basic features of the Kumakhov optics.

         In figure 1, reflection of a photon from a smooth surface is illustrated.

A photon is incident at an angle of Θ_in< Θ_c. Critical angle of reflection or Fresnel angle equals

                                                   Θ_c=hw_p/E                       (1);

         where w_{p –}plasma frequency of reflective surface, E-photon energy. For glass - hw_p≈30 eV, that is E=1 keV, Θ_c=3x10^-2 radian. Consequently, if E= 10 keV ; Θ_c=3x10^-3 radian.

In figure 2, photon moving in a channel, comprised by two reflective surfaces, is presented.

When a channel involves a glass tube or a monocapillary- we have photon “channeling”.

In figure 3, photon bending between two surfaces, as the result of multiple reflections, is shown.

The revised successful experiments on bending x-radiation by means of glass monocapillaries were conducted by M. Kumakhov team³.

For photon bending in a channel it is important for the radius of channel bending to refer to:

                                            R>R_c = 2d / Θ_c²                                                  (2);

where d is the diameter of channel.

This is quite a big radius. For example,

if d=0,5mm and E=1keV (Θ_c » 3x10^-2 radian) –

R_c» 10³mm= 10²cm. Increasing energy E, will increase R_c, quadratically, due to the equation Θ_c² » 1/E².

         Let us point out that in the examples cited, in straight, bended and tapered monocapillaries, the critical capture angle of source radiation does not exceed 2 Θ_c,that is- two critical angles of reflection. The angle is rather small. Thus, from an isotropic source the mentioned optics subtracts a negligible part of energy:

         Let us suppose that there is an X-ray tube with a Cu anode (E» 8 keV,

Θ_c = 4·10^-3 radian). Then, from the isotropic source with the intensity I_0,a small part of energy ‘h’is subtracted, which equals to:

h = I₀ * (Θ_c)² * (π/4π) = I₀ * 16 *10^-6 =   I₀ * (4*10^-6)

                                                                           4                                         (3);

It means that, in monocapillary optics, only several parts per million – a negligible part of the source radiation - is used.

         The essence of Kumakhov optics is presented in figures 4-6.

         From an isotropic source l₀ part of the radiation is captured by the system of bended surfaces. Bended monocapillaries can be taken as bended surfaces. Let us, now, mention the most important features:

1)     the peripheral bended channels 1 and 1’ capture radiation at a rather wide angle, relating to the centroidal axis,

2)     the closer bended channel lies to the centroidal axis - the smaller the angle is, relative to the centroidal axis, at which a channel captures radiation from the source,

3)     every channel, including the central non-bended channel, is positioned so, that the direction of photons entering the channels, has the angle smaller than the critical angle of reflection, relating to the internal channel surfaces.

4)     In the meantime, the radii of bending increase, on reaching the centroidal axis.

         The system, presented on figure 4, transforms the radiation, divergent from the source, into quasiparallel beam. To solve it, as appears from the figure, a certain system of specifically oriented waveguides with different radii of curvature and different bending angles is used. It is a fact, peripheral channels 1 and 1’ bend radiation at a wider angle than channels 2 and 2’. The bending angle of radiation is:

                                       (4);

where l – channel length, R – radius of curvature.

If we propose that lengths of the channels in the outlined system are somewhat analogous, then, the radius increases as bending angle decreases. The system in figure 4 was called a “half-lens”.

In figure 5, a complete lens is pictured, - it features a symmetrical extension of a “half-lens”. The lens itself focuses radiation from source l₀.

Fig.5 Focusing of a divergent beam

Kumakhov Polycapillary Optics

         Formula (2) presents interrelation between a diameter of a channel, radius of channel curvature and energy transported through a channel (Q_c ~ 1/E²).

It is evident from the equation: with photon energy of E= 30 keV, Q_{c
=} 10^-3 rad and the channel diameter d=.0,5mm, the radius of channel curvature must be ~100 m. With such radius of curvature the radiation bending ,even through a small angle /~10^-2rad/, would demand a sizable length.

The bending angle φ equals to:

                                                                                             (5);

therefore, with φ=10^-2, R=100, we obtain l = 1m.

The length is, excessively, sizable! To bend radiation through the angle of 10^-1 radian, we must have the length of 10m.

         Consequently, decreasing diameters of channels was necessary.

A channel decreased in diameter down to 300 microns and less, would start “hanging” in the air.

It is difficult to control a capillary, mechanically. Diameter of a human hair is, approximately, 100 micron. Though a human hair has blind structure, as distinguished from a hollow capillary, the first is similarly complicated to control, mechanically.

Both, a capillary and a human hair, are impossible to “force” assuming a necessary shape.

Therefore, rises the problem of a dramatic decrease of a capillary diameter for the purpose of:

obtaining the capability of focusing photons of high energies (over dozens of keV);

producing lenses, with applicable geometrical dimensions.

It is clear that lenses required not only small capillaries. The channels needed also to be curved, under a specific rule.

The diameters of channels had to modify, as well. The solution for the problem was suggested by M. A. Kumakhov^9-10.The lenses, which met the mentioned requirements, for the first time, were created in his laboratory.

The optics was, later, named Kumakhov polycapillary optics. The foregoing are some major features of the optics:

Figures 6-8 illustrate the technical peculiarities. Initially, the sizable tube is taken (its diameter can vary from several millimeters to several centimeters).

At first stage, the tube is drawn at high temperatures in a furnace, and a monocapillary is obtained with a diameter of 1mm or less (fig. 6).

     At the second stage a substantial number of such monocapillaries is, once again, put into a big channel and drawn down to 1mm and less.

As a consequence a polycapillary is produced (fig. 7).

A polycapillary - is a tube, where a great number of channels are sintered together. This is a monolithic system.

Ordinarily, a 1mm polycapillary contains, approximately, 1000 channels

/with diameter ~10-20 microns/.

For producing a lens, the presented capillaries are placed into a tube of ³1mm in diameter and drawn, while    formed the certain shape. That way, a monolithic polycapillary lens is created (the 4^th generation lens)

     When a large number of monocapillaries of ≤1mm is placed into a large tube and the tube is drawn, while   shaped a certain form, then a monolithic monocapillary lens is created (the 3^rd generation lens).

When polycapillaries are placed into a large tube and drawn into a small straight polycapillary of »1mm, the micron and submicron channels are likely to be created in such polycapillary (fig. 8).

Given polycapillaries, placed into a large size tube and drawn, as well, by a certain method, develop an integral lens (the 5th generation lens).

All the outlined systems were obtained and tested in the Kumakhov laboratory, for the first time.

5 Generations of X-Ray Lenses

In figure 9, the focusing process with the lens, which consisted of 2000 capillaries, is shown.

Fig.9

The focal spot is about 5cm remote from the lens exit. Density at focal point was by an order higher than at the at lens entrance – thus, we have the precise focusing effect. In figure 10, the photo of the first assembled monocapillary lens is presented.

Fig.10

Lenses, assembled from polycapillaries

A polycapillary – is a tube of 1mm in diameter, where multiple (about 1000) channels are imbedded.

The polycapillaries give the opportunity of focusing higher energy radiations. The very lenses appear by means of the technology, analogous to that, for the lenses assembled from monocapillaries.

Monolithic monocapillary lens

The latter lens is created by the subsequent method:

Monocapillaries of 1-0,4mm in diameter are placed into a tube with a diameter from one to several centimeters. Thereafter the tube is put into a specific temperature pattern and drawn, while, at the same time, being formed up. The first monolithic lens was produced in the Kumakhov laboratory in the 1980s.

Such systems were part of a number of experiments on focusing and diffraction at energies up to 10keV. The normal diameters of channels in the very lenses were from one hundred to several hundreds micron.

Monolithic polycapillary lens

         The pointed instrument, like the monolithic monocapillary lens was assembled, first, in the Kumakhov laboratory in 1980s.

In the beginning, several profound problems took place, as only the central part of the polycapillary “worked”. Much effort was applied for having lenses perform well. Such lenses were well used.

         The development of Kumakhov optics read in over 30 articles at international conferences in 1988 and 1990^11-12, and the SPIE proceedings and reviews in 1991-1999^13-18.

The lenses “work”, perfectly, with energies from several keV to 30keV. The mentioned polycapillary lenses are well employed in the XRF investigation and diffractometry. Famous international suppliers, such as Bruker, Panalytical, Rigaku, Unisantis, Shimadzu, others, use polycapillary lenses in the marketed products. Around five thousand various units, based on the Kumakhov monolithic polycapillary lens, exist, nowadays, in the world. The devices on the basis of polycapillary optics have appeared to be most popular due to the facts, presented further:

polycapillary optics, in comparison with the diffraction and refraction optics, has a wide capture angle. The ordinary capture angle is 0,1-0,15 rad. A 0,1 rad. angle is 50 times wider than the critical angle in the line of Мо (17keV), in which the majority of the XRF analyzers perform,

polycapillary optics appears to be universal, because of portability. Diameter of a lens can be ≤1cm, length - ≤10cm. Lenses can simply be integrated into devices,

polycapillary optics proves to be wide band; which is extremely preferable in an XRF analyzer. At once, the very optics, effectively, suppresses high energies,

polycapillary optics proves to be inexpensive and pay back fast,

owing to the optics, decreasing source power is potential. A microfocusing source of 50Watt with a lens has greater efficiency than a 5keV rotating anode. A rotating anode demands a particular premise, important cooling systems and screening. Unlike it, a microfocusing source may be located at any premises,

because of polycapillary optics it is eventual, to have equipment featuring numerous functions. Likewise, on mechanical basis alone, the first unit combining the function of an XRF and possibilities of diffractometer, and a device, performing the operations of a stress-analyzer and an XRF, were created at IRO.

Kumakhov Polycapillary Neutron Optics

The first neutron lens

The first polycapillary neutron lens was created in the laboratory of                      Prof. M. A. Kumakhov at the Kurchatov Institute for Atomic Energy in the 1980s¹⁹.         The lens is depicted in figure 11 (from the “Nature” magazine, vol. 357, pp. 390,391, 1992).

Fig.11

                   The lens contained 721 polycapillary. Each polycapillary consisted of about 1000 channels, - that is, the lens included more than 700,000 channels.

This lens was produced from glass without boron atoms.

The length was 20cm,

focal distance ~ 10cm,

diameter of entrance – 29mm,

diameter of exit – 15mm.

The initial experiments were undertaken on the reactor IR-8 at the Kurchatov Institute for Atomic Energy. The lens increased neutron fluxes sevenfold.

Bender of thermal neutrons and X-rays

                   Based on the Kumakhov polycapillary optics, an instrument was created to bend the neutron and X-ray beams. The device allows bending the mentioned beams through large angles (up to 30 degrees) at small lengths of systems (15- 20 cm). The length of the bender depends on the neutron and X-ray energies and on the bending angle. The typical length for bending angles of 10-15 degrees is      10-15 cm with standard energies for thermal neutrons and energies of 5-15keV for X-rays.

                   The diameter of the bender depends on diameters of neutron and X-ray beams. The cross-section of the bender is analogous to the cross section of the beam (it may be square, rectangular, round, etc.) sp;

Experiments on bending a neutron beam

The neutron bender, created at Institute for Roentgen Optics was applied for bending a neutron beam from a reactor at the Hann-Meitner Institute (Berlin)²⁰.

Several results of the experiment are presented in figure 12.

Fig. 12

At the length ~ 15cm a neutron beam with high efficiency (about 20%) was bended through an angle of about 20⁰. When bended through an angle =10⁰ ,the efficiency constitutes 35%. Thus, polycapillary optics, effectively, allows bending neutron beams through high angles with small lengths given (about 15cm).



Experiment on focusing a neutron beam using          big assembled neutron lens

         In the beginning of 1990-s at Institute for Roentgen Optics ,IRO, the big assembled neutron lens was created. This lens had the following parameters:

Lens entrance – 6.5 cm х 5 cm

Lens exit -         4.5 cm x 3 cm

This big neutron lens contained over tens of millions of channels.

It was applied in focusing the neutron beams at the reactor in Julich (Germany) in 1996.

The experiment was successful. The neutron lens allowed engineers to increase densities of neutron beams by the factor of about 60.

The photo of the lens is presented in figure 13.

Fig. 13

Evolution of Kumakhov neutron

polycapillary optics

                   The technology for neutron optics, in fact, coincides with the polycapillary X-ray optics technology. Initially, assembled monocapillary lenses were created; further, solid monocapillary and polycapillary neutron lenses were introduced.

The optimistic results were achieved during the use of these lenses at atomic reactors all over the world. A large number of experiments were undertaken in Russia (Kurchatov Institute for Atomic Energy), USA (NIST), Germany (Berlin, Julich, Munich), Switzerland, France, etc²¹.

Table 1 presents the parameters of monolithic polycapillary neutron lenses that were studied at the reactor   in Obninsk (the Russian Federation).

Summary

The neutron optics may be applied in the following spheres and fields:

1. Creation of pure thermal neutron fluxes.

2.     Activation analysis.

         3.    Neutron microscopy.

4.    Neutron boron-capture therapy.

         5.    Polycapillary optics is greatly efficient in X-ray devices On the basis of the very                             optics a new generation of X-ray spectrometers, diffractometers, reflectometers, etc.                with excellent effectiveness has been created.

6.    Correspondingly, based on polycapillary neutron optics, it is possible to develop the new range of devices for neutron beams.

References

F. Jentzch, E. Nahring, Z. Tech. Phys. (Leipzig) 12, 185 (1931).

R.V. Pound and G.A. Rebke, Phys. Rev. Lett. 3, 554 (1959).

M. A. Kumakhov, A. Kolomiitsev, and Yu. Tchertov, Poverknost N10, 25 (1986).

M. A. Kumakhov, A. Kolomiitsev, and Yu. Tchertov, Poverknost N2, 44 (1987).

M. A. Kumakhov et.al. Pis’ma Zh. Tekh. Fiz. 13, 257 (1987) [SOv.Tech.Phys.Lett 13, 105].

P. Engstrom, S. Larsson, A. Rindby, and B.Stocklassa. Nucl. Instrum. Methods Phys. Res. B 36, 222 (1989)

D.J. Thiel, D.N. Bilderback, A. Lewis, and F.A. Stern, Nucl. Instrum. Methods Phys. Res. A 317, 547 (1992).

D.A. Carpenter, X-Ray Spectrom. 18, 253 (1989).

^9. M. A. Kumakhov, USSR Certificate of Authorship N 1322888               (July 26, 1984).

^10. M. A.      Kumakhov, Radiation of Channeling Particlesin Crystals (Energoatomizdat, Moscow, 1986).

^11. Abstracts of III Conference on Radiation of Charged Particles in Crystals, Elbrus, 1988.

^12. Abstracts of IV Conference on Radiation of Charged Particles in Crystals, Elbrus, 1990.

^13. M. A.      Kumakhov and F.F. Komarov, Phys. Rep. 191, 299 (1990).

^14. W. M. Gibson and M. A.      Kumakhov, McGraw-Hill Yearbook of Science and Technology (McGraw-Hill, New York, 1993), p. 488.

^15. M. A.      Kumakhov, Proc. SPIE 2011, 193 (1993).

^16. M. A.      Kumakhov, Proc. SPIE 2859, 116 (1995).

^17. M. A.      Kumakhov, Proc. SPIE 3113, 362 (1997).

^18. S.V. Nikitina, A. S. Scherbakov, and N. S. Ibraimov, Review of Scientific Instuments, v.70, N7, pp.1-7 (1999).

^19. M. A.      Kumakhov, V. Sharov, Nature, v.357, pp. 390-391, 1992.

^20. A. Ioffe, S. Dobagov, M. Kumakhov, Neutron News 6, p.20, 1995.

^21. M. A. Kumakhov, Nucl. Instrum. Methods Phys. Res. A 529, 69-72, 2004.