# Design of a source of quasi-monochromatic x-ray radiation on the basis of a proton accelerator, fitted with an X ray-optical system.

1. IntroductionThe development of new directions in science and technology (nanophysics and nanotechnology, genomics and proteomics, etc.), requires the development of instrumental methods and equipment for investigating the composition and structure of the materials, including biological objects, with spatial resolution in the nanometre range. Nuclear-physical methods using accelerators offer these possibilities. New sources of synchrotron radiation (SR) make it possible to investigate the submicron region in operation in the x-ray range and use the latest achievements of x-ray optics.

Taking into account the unique nature and high cost of the sources of synchrotron radiation, extensive investigations are being carried out into the development of compact laboratory sources of x-ray radiation with the focusing of electron beams of micron dimensions and with current of several milliamperes. It was shown in [1, 2] that the application of the liquid metal jet as the target has made it possible to produce the brightness of the x-ray source on the level of

[10.sup.10] photons/[s x [mm.sup.2] x [m.sup.rad2]0.1%BW

The principal problem of the sources in which x-ray radiation is generated under the effect of electron beams, is the high level of the braking radiation (bremsstrahlung) of the electrons (Fig. 1b). To construct sources of monochromatic radiation, it is necessary to use filters or monochromators and this reduces the intensity.

The Institute of Applied Physics of the National Academy of Sciences of Ukraine has been carrying out investigations to produce proton beams with the energy of the order of MeV, with micron dimensions. Fig. 2 shows the analytical accelerator complex (AAC) of the Institute of Applied Physics [4] with a channel with the resolution of 2 [micro]m [5]. The application of the proton beams with the energy of 1-2 MeV produces the yield of ^-radiation identical with the electron beam of 30-50 keV (Table 1), but the bremsstrahlung background is approximately halved and, consequently, it is not necessary to use filters or monochromator.

In this year, in cooperation with the Institute of Problems of Technology of Microelectronics and Special Purity Materials (IPTMiOM, Russian Academy of Sciences, Chernogolovka) within the framework of the project with the Russian Federation work started in the electrostatic accelerator of the Institute of Applied Physics of the National Academy of Sciences of Ukraine, with the energy of 2 MeV t construct a source of quasi-monochromatic x-ray radiation. The first stage will include the investigations on solid converters, with the beam current of 100 (A, the second stage the investigations with liquid-jet targets with the beam currents of approximately 1 mA.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

2. Determination of the yield of x-ray radiation under the effect of the proton beam

It is well-known [3] that the yield of x-ray photons from a thin layer, recorded by a detector, is determined by the expression:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1.1)

where S(E) is the braking capacity of the target material, measured in [10.sup.-15] eV x [cm.sup.2]/atom, the values are taken from [6]; co is the fluorescent yield, values taken from [7]; [sigma](E) is the ionisation cross-section at the proton energy E; N is the number of protons; 8 and d[omega] are the efficiency and solid angle of the detector; u is the linear coefficient of attenuation, the values are taken from [7-9]; [alpha] and P are the generalised angles between the normal to the target and the direction of movement of the proton and the x-ray photon, respectively (Fig. 3); [E.sub.0] is the initial energy of the proton.

The total recorded yield is determined by integrating (1.1). In this case it must be taken into account that there is some proton energy [E.sub.cr] at which the proton may still cause ionisation of the target atoms.

The total yield of the protons in 1 s in the solid angle 1 steradian is equal to:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1.2)

where e is the electron charge, I is the proton beam current.

There are several theories which can be used to calculate the differential ionisation cross-section.

The differential ionisation cross-section of the S-shell of the atom of the target (S = K, L, M, ...) in the Born approximation of planar waves (PWBA) [10]: is.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1.3)

where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] the dimensionless parameters [[theta].sub.s] and [[eta].sub.s] represent the reduced binding energy of the electron and the reduced proton energy; a0 is the radius of the first Bohr orbit of the hydrogen atom; [Z.sub.S] = Z-0.3; [I.sub.S] is the binding energy of the S-shell; R = 13.6 eV is the ionisation energy of the hydrogen atom; m and M is the mass of the electron and the proton, respectively; E is the proton energy; the function [F.sub.s]([[eta].sub.s]/[[theta].sup.2.sub.s], [[theta].sub.s] was tabulated in [10].

[FIGURE 3 OMITTED]

The differential cross-section in the Born approximation of the planar waves (PWBA) with the corrections for the energy losses (E), Coulomb deviation (C), perturbed stationary states (PSS) and relativistic (R) effect (ECPSSR) [11] is in good agreement with the experimental data:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1.4)

where [q.sub.0S] is the minimum value of the momentum transferred by the incident particle to the target atoms; [[zeta].sub.S] is the correction for the binding energy of the electron; d is half the distance of maximum convergence; [[??].sub.S] and [[??].sub.S] is [[eta].sub.S] and [[theta].sub.S]S of the PWBA theory with corrections.

The resultant values of the yield of x-ray radiation of K-series for the targets produced from copper and titanium are presented in Table 2.

2.1. Comparison of the calculated yield with experimental values

Taking into account the fraction of the photons of the K-series, relating to the [K.sub.[alpha]]-line of copper, the calculated value of the yield for the beam current of 100 pA and [omega] = 5 x [10.sup.-3] steradian [omega] x N (1 MeV) = 32 photons/s, and the value obtained in the channel of the nuclear microprobe 50 photon/s (Fig. 4).

The experimentally measured value of the yield of x-ray radiation in the same channel made of a zirconium target QN (1 MeV) = 1.1 x [10.sup.-9] photons/proton, and the calculated value of the yield is Q x [N.sub.lexp] (1 MeV) = 0.82 x [10.sup.-9] photons/proton (for ECPSSR) and Q x [N.sub.1] (1 MeV) = 1.23-[10.sup.-9] photons/proton (for PWBA). The identical relationship was published in [12].

2.2. Dependence of the yield of x-ray radiation on the angles and

Small changes of the angles result in a change of the yield, as shown in Table 3.

The calculations are important for practical application of various beam-specimen-detector geometries [3].

[FIGURE 4 OMITTED]

2.3. Evaluation of the bremsstrahlung background

As shown in [13], the background of bremsstrahlung of the protons is considerably smaller than the background of bremsstrahlung of electrons (as a result of the factor 1836).

The bremsstrahlung of the electrodes, emitted during inelastic collisions, consists of three components: secondary electron bremsstrahlung (SEB), bremsstrahlung of quasi-free electrons at high proton velocities (QFEB) and bremsstrahlung of the atoms in return of the emitted electrons to the initial bonded state [14].

A large amount of data was published in [13] for theoretical description of the SEB and the overall effect of bremsstrahlung background.

Another source of the background is [gamma]-radiation from nuclear reactions [3]. For 5 MeV protons the background becomes considerably stronger as a result of reactions caused by photons.

3. Determination of the yield of x-ray radiation under the effect of the electron beam

The number of the photons recorded by the detector and leaving the thin layer into the solid angle of 1 steradian and relating to 1 electron is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.1)

where [eta] is the fraction of the back-scattered electrons [15]. Equation (2.1) takes into account the attenuation of the beam during the passage of the electrons as a result of their backscattering.

As shown in [15], the fraction of the back-scattered electrons depends on Z and is almost independent of energy:

n = -0.0254 + 0.016Z-1.86 x [10.sup.4] [Z.sup.2] +8.3 x [10.sup.7] [Z.sup.3]. (2.2).

To calculate the ionisation cross-section we can use the equation derived by Bethe [16]:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.3)

where E is the energy of the electrons in the beam, Enl is the binding energy of the electrons in the nl-shell, [Z.sub.nl] is the number of the electrons in this shell, [b.sub.nl] and [c.sub.nl] are the Bethe parameters for the nl-shell. For the K-shell [b.sub.k] [??] 0.90 and [c.sub.k] = 0.60-0.75 in the energy range 4 < E/[E.sub.nl] < 25.

The braking capacity of the element is determined from the Bethe equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.4)

where the mean ionisation potential is J = (9.76Z +58.5 [Z.sup.-019]) x [10.sup.-3] keV, n is the number of atoms in the unit volume. The total observed the yield is determined by integrating (2.1):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.5)

Here, it should also be taken into account that there is some electron energy [E.sub.cr] at which the electron may still cause ionisation of the target atoms.

3.1. Comparison of the calculated yield with experimental values

The yield of x-ray radiation of the K-series from Cu at the selected parameters ck = 0.75, [epsilon] = 1, [alpha] = 0[degrees], [beta] = 45[degrees], n = 0.3024 is shown in the third column in Table 4. For the geometry [alpha] = 0[degrees], [beta] = 45[degrees] at ck = 0.65 we calculated the dependence of the yield of the photons from Ti on accelerating voltage U (Table 5).

For the beam current of I = 10 [micro]A and U = 40 kV in the reflection geometry, the yield N(40) = 3.47 x [10.sup.10] photons/s x ster]. In [18] the following values obtained for the same current and voltage in the streaming geometry: N (40) = 1.62 x [10.sup.9] photons/s x ster. photon/s x ster

3.2. Evaluation of the bremsstrahlung background

As shown in [15], the yield of x-ray radiation values obtained on the basis of the experiments [17], have the following form (taking into account the losses due to reflection):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.6)

where i is the beam current, n ~ 1.67. The background of continuous bremsstrahlung is described by the equation:

[I.sub.H] ~ iZ([E.sub.0] -E)/E. (2.7).

The ratio of the intensity of characteristic radiation to the intensity of continues radiation inside the same energy range is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.8).

Assuming that the energy of the continuous spectrum in which we are interested is E [approximately equal to] [E.sub.cr] , we obtain:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2.9)

The ratio of the peak to the background at the electron beam energy of 30 keV in copper is: [I.sub.x]/[I.sub.n] = 1/9 [(30 - 8.979/8.979).sup.1.67-1] [approximately equal to]

4. Evaluation of the brightness of the source

Previously, the value of the yield from titanium on the basis of the proton accelerator was N = 2 MeV), = 5.57 x [10.sup.12] photons/s x ster. The brightness of the [K.sub.[alpha]]-doublet for this value of the proton flux is B = 4.46 x [10.sup.6] photons/s x [mm.sup.2] x [mrad.sup.2], if the size of the spot is assumed to be 1 mm2 [4]. The spectral brightness for the [K.sub.[alpha]-doublet of titanium is estimated from the natural width of the line [19]:

[B.sub.[gamma]] = 1.28 x [10.sup.7] photons/s x [mm.sup.2] x [mrad.sup.2] 0.1 BW. These values of the brightness is typical of x-ray tubes.

If the proton beam is focused to the size of 10 x 10 [micro][m.sup.2], we obtain [B.sub.[gamma]] = 1.28 x [10.sup.11] photons/ s x [mm.sup.2] x [mrad.sup.2] 0.1 BW. This corresponds to the beginning of the brightness range of synchrotron sources on deflecting magnets.

Fig. 5 shows the model of the source of quasi-monochromatic x-ray radiation based on a proton accelerator fitted with an X Ray-optical system.

5. Conclusions

The yield of x-ray radiation under the effect of the protons and electron beams from different converters was calculated. The results show a considerably smaller background of bremsstrahlung for the protons at the same yield of the photons the particle and the energies of 1-2 MeV of the proton beam and 20-50 keV of the electron beam. The calculated yield was compared with the experimental values, measured in the channel of a nuclear microprobe. A model of the source of quasi-monochromatic x-ray radiation is proposed with justification of the advantages of using the proton beam instead of the electron beam. The brightness of the source and methods of increasing it have been evaluated. The experimental base for the given project is discussed.

[FIGURE 5 OMITTED]

References

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L.G. Shabel'nikov, V.L. Denisenko *, M.V. Il'yashenko *, V.E. Storizhko *, A.A. Drozdenko * and S.A. Vershinskii *

Institute of Problems of Microelectronic Technology and Special Purity Materials, Russian Academy of Science, ul. Institutskaya 6, 142432 Chernogolovka, Russia

* Institute of Applied Physics, National Academy of Sciences of Ukraine, ul. Petropavlovskaya 58, 40030 Sumy, Ukraine

Table 1. Comparison of the yield of photons from the electron and proton beams Electrons Protons ([C.sub.k] = 0.65) Yield, photons/ particle * ster 1 MeV 2 MeV 30 keV 40 keV [N.sub.1](Cu) 0.10* 1.66* 1.26* 2.6* [10.sup.-4] [10.sup.-4] [10.sup.-4] [10.sup.-4] [N.sub.1](Ti) 0.85* 8.10* 3.70* 5.55* [10.sup.-4] [10.sup.-4] [10.sup.-4] [10.sup.-4] Table 2. Yields of x-ray radiation from Cu and Ti at [epsilon] = 1, / = 1 mA, [alpha] = 0[degrees], [beta] = 45[degrees] E, MeV N(Cu), 10 (12) photons/(s*ster) N(Ti), 10 (12) photons/(s*ster) PWBA ECPSSR PWBA ECPSSR 1 0.076 0.064 0.72 0.53 2 1.06 1.03 5.57 5.06 Table 3. Yields of x-ray radiation from Cu and Ti at [epsilon] = 1, / = 1 mA, [alpha] = 0[degrees], [beta] = 45[degrees] Variation [alpha] = 0[degrees], [alpha] = 45[degrees], [beta] = 45[degrees] [beta] = 0[degrees] 2[degrees] in 0.006% 0.190% angle [alpha] 2[degrees] in 0.380% 0.003% angle [beta] Target rotated 0.348% 0.187% by [2[degrees] Table 4. The yield of x-ray radiation of K-series from Cu, photons/ (electron *ster) Voltage, kV 15.5 20.2 25.2 30.1 35.2 40.0 Theoretical, 0.37 0.83 1.38 1.99 2.65 [10.sup.-4] [17] Experimental, 0.41 1.09 1.97 3.13 4.32 5.84 [10.sup.-4] [17] This work, 0.10 0.47 1.05 1.72 2.49 3.23 [10.sup.-4] Table 5. Dependence of the yield of photons from Ti on acceleration voltage U Voltage, kV 20 40 60 80 100 120 140 [10.sup.-4] Yield, 1.85 5.55 7.65 7.85 7.16 6.33 5.63 photons electron* ster Voltage, kV 160 180 [10.sup.-4] Yield, 5.08 4.65 photons electron * ster

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Title Annotation: | INTERACTION OF RADIATION AND PARTICLES WITH CONDENSED MATTER |
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Author: | Shabel'nikov, L.G.; Denisenko, V.L.; Il'yashenko, M.V.; Storizhko, V.E.; Drozdenko, A.A.; Vershinski |

Publication: | Physics of Metals and Advanced Technologies |

Article Type: | Report |

Geographic Code: | 4EXUR |

Date: | Jan 1, 2010 |

Words: | 3021 |

Next Article: | Spatial scaling in the theory of X-ray scattering. Non-standard dynamic theory. |

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