1414 IEEE JOURNAL OF SELECTED TOPICS IN QUANTUM ELECTRONICS, VOL. 10, NO. 6, NOVEMBER/DECEMBER 2004 Compact High-Brightness Soft X-Ray Cherenkov Sources Walter Knulst, Jom Luiten, and Jan Verhoeven Invited Paper Abstract—Compact narrow-band high-brightness soft X-ray tube generally not very attractive as a source. Recent devel- sources based on the Cherenkov effect are very promising. We dis- opments in this direction are, for instance, an extreme ultravi- cuss the theoretical basis for this novel electron-accelerator-based olet (EUV) tube producing silicon L-band fluorescence radia- source. We present results of experiments, which confirm the the- oretical expectations and demonstrate that intense narrow-band tion (centered at 92 eV) [2] and a liquid-water-anode producing Cherenkov light can be produced at the silicon L-edge (99.7 eV) oxygen K -fluorescence radiation (525 eV) [3]. and, in the water window, at the titanium L-edge (453 eV) and the More intense, but still compact, alternatives are plasma-based vanadium L-edge (512 eV). On the basis of theory and experiment, sources, which cover the range from visible radiation up to we show that a compact high-brightness Cherenkov source may X-rays of a few kiloelectronvolts. Over the last decade, the ef- be realized, which fulfills the requirements for practical soft X-ray microscopy and photoelectron spectroscopy. ficiency of these soft X-ray sources has improved enormously. Plasma-based sources can be divided into pinch plasma (PP) Index Terms—Cherenkov effect, extreme ultraviolet (EUV), pho- and laser-produced plasmas (LPP). PP sources, in which a high toelectron spectroscopy, soft X-rays, X-ray microscopy. current pulse is sent through a plasma to make it collapse, are presently the only sources capable of producing the average I. INTRODUCTION power levels at 13.5 nm required for industrial high-throughput RESENTLY, the soft X-ray sources with the highest EUV lithography. In LPP sources nanosecond laser pulses brightness (number of photons per second, per unit area, are used to create plasmas, emitting line spectra from highly P ionized atoms such as C, N, O, or Xe. As a side effect, these per unit solid angle, and per unit relative bandwidth) are those based on undulators in storage rings. Many powerful sources produce a certain amount of debris, which can be soft X-ray techniques which require high brightness, such as reduced by using gaseous or liquid targets [4], [5]. Recently, X-ray microscopy, X-ray crystallography, X-ray diffraction, it has been shown that LPP sources are sufficiently bright for and fluorescence X-ray microprobes, are therefore limited to practical imaging in the water window [8]. these synchrotron light facilities. However, several of these A relatively recent development is the high-harmonic (HH) applications require substantially less than the brightness levels source: when a very short, highly intense laser pulse is sent offered by undulator radiation, so with further development through a gas, very high odd harmonics of the frequency of the of alternative sources they may become available to smaller incident laser pulse are generated by nonlinear interaction [6]. institutes as well. This possibility has sparked a great deal The conversion efficiency to high photon energies, however, is of interest in compact (laboratory-sized) high-brightness soft generally limited by the lack of phase matching. Recently, proper X-ray sources [1]. phase matching has been extended into the water-window region The most well-known compact X-ray source is the X-ray [7]. HH sources operating at 13 nm are presently sufficiently tube, which has been used in many fields of research ever since bright for practical imaging [9]. the discovery of X-rays by Röntgen. However, the emission in- Compact electron-accelerator-based sources [10] have tensity of fluorescence radiation in the soft X-ray region, which received relatively little attention until now. Among the in- requires low-Z materials, is very low, making the soft X-ray teractions of relativistic electrons with a medium that cause emission of radiation, such as transition radiation (TR), chan- neling radiation and parametric X-rays, especially Cherenkov radiation (CR), is a promising candidate for a compact soft Manuscript received May 4, 2004; revised August 24, 2004. This work was supported by the Technology Foundation STW, applied science division of X-ray source. As we will show in this paper, in the soft X-ray NWO, and the technology programme of the Ministry of Economic Affairs, region the Cherenkov radiation is characterized by a single-line The Netherlands. spectrum and by forwardly directed emission and only requires W. Knulst is with Delft University of Technology, 2600 AA Delft, The Netherlands. low-relativistic electrons from a laboratory-sized accelerator. J. Luiten is with Eindhoven University of Technology, 5600 MB Eindhoven, Cherenkov radiation is emitted by a charged particle if its The Netherlands. velocity exceeds the phase velocity of light in a medium J. Verhoeven is with the FOM Institute for Atomic and Molecular Physics, 1098 SJ Amsterdam, The Netherlands. and is therefore limited to the wavelength regions Digital Object Identifier 10.1109/JSTQE.2004.837738 where the real part of the refractive index exceeds unity . 1077-260X/04$20.00 © 2004 IEEE KNULST et al.: COMPACT HIGH-BRIGHTNESS SOFT X-RAY CHERENKOV SOURCES 1415 Cherenkov radiation is emitted at an angle with respect to the II. THEORY OF SOFT X-RAY CHERENKOV RADIATION electron trajectory which is given by A. Ginzburg–Frank Theory When a relativistic electron is sent through a foil, several ra- (1) diation phenomena occur. Due to the fact that the Cherenkov radiation is generated in a finite solid-state medium, it is always accompanied by transition radiation, which is generated by the In the visible region Cherenkov radiation is a well-known effect, electron at the medium-vacuum interfaces. Therefore, this effect which is often applied in high-energy particle detection [14]. In has to be taken into account as well. All other radiation phe- the soft X-ray region, however, the refractive index is generally nomena, such as fluorescence radiation, Bremsstrahlung, and smaller than unity and materials are highly absorbing. There- visible transition radiation are discussed in the context of the fore, Cherenkov radiation in the soft X-ray region was excluded experimental results in Sections III–V. for a long time. In 1981, Bazylev et al. [11] realized, however, Until now, only a few theoretical studies [16], [17] have that at some inner-shell absorption edges the refractive index addressed the possibility of generating soft X-ray Cherenkov exceeds unity, implying that Cherenkov radiation can be gener- radiation at inner-shell photon energies. We start the analysis ated in a narrow-band region around certain absorption edges. from the Ginzburg–Frank equation [20], [21], [18], which was They demonstrated this experimentally for the carbon K-edge initially intended to describe transition radiation only. As this (284 eV), using 1.2-GeV electrons. Later, Moran et al. [15] equation is the exact solution of Maxwell’s equations in a showed that Cherenkov radiation is emitted by 75-MeV elec- system consisting of two adjacent semi-infinite dielectric media, trons in silicon at the L-edge (99.7 eV) and in carbon at the it automatically describes Cherenkov radiation as well. K-edge. Recently, we have shown that Cherenkov radiation at Suppose an electron moves through the interface between a the silicon L-edge can be generated with 5-MeV electrons [12] medium with dielectric constant and vacuum. The number of and at the titanium and vanadium L-edge with 10-MeV elec- photons emitted into the vacuum per electron, per unit band- trons [13]. It turns out that the potential brightness of this new width, and per unit solid angle, the so-called spectral angular type of compact source is sufficient for imaging applications. yield, is given by [18], [20], and [21] In this paper, the theoretical and experimental aspects of gen- erating soft X-ray Cherenkov radiation and its potential as a high-brightness source are treated in somewhat more detail than in the first brief reports [12], [13]. This paper is structured as follows: In Section II, the theory (2) of soft X-ray Cherenkov radiation is presented. Although the electromagnetic theory of Cherenkov radiation was formulated with the relative electron velocity and the fine struc- already a long time ago by Frank and Tamm [19], this theory ture constant. Using Snell’s law for a nonabsorbing medium does not apply anymore in the soft X-ray regime because of the , it is easy to see that the factor strong absorption of materials. Instead, a description is required in the denominator becomes zero and, thus, the spectral an- in terms of the Ginzburg–Frank equation, which was originally gular yield is infinite at exactly at the Cherenkov angle [see developed for transition radiation [20], [21]. In Sections III–V, (1)]. This is due to the fact that in the case of a semi-infinite the measurements of soft X-ray Cherenkov radiation are pre- medium Cherenkov radiation is generated over an infinite path sented. The main purpose of the experiments is to demonstrate length. However, in reality, either the path length is finite or that moderate electron energies are already sufficient to gen- the medium is absorbing, making the Cherenkov yield finite. In erate narrow-band soft X-ray Cherenkov radiation in different the soft X-ray regime all media are strongly absorbing, which materials. We have firmly established the generation of silicon is taken into account by a complex-valued dielectric constant: L-edge Cherenkov radiation with 5-MeV electrons (Section III) .