Patent Publication Number: US-9847618-B2

Title: Laser apparatus

Description:
TECHNICAL FIELD 
     The present disclosure relates to a laser apparatus. 
     BACKGROUND ART 
     In recent years, as semiconductor processes become finer, transfer patterns for use in photolithographies of semiconductor processes have rapidly become finer. In the next generation, microfabrication at 70 nm to 45 nm, and further, microfabrication with 32 nm or less will be demanded. In order to meet the demand for microfabrication at 32 nm or less, for example, the development of an exposure apparatus in which an apparatus for generating extreme ultraviolet (EUV) light at a wavelength of approximately 13 nm is combined with a reduced projection reflective optics is expected. 
     As the apparatus for generating EUV light, three types of apparatuses have been proposed, which include a Laser Produced Plasma (LPP) type apparatus using plasma generated by irradiating a target material with a laser beam, a Discharge Produced Plasma (DPP) type apparatus using plasma generated by electric discharge, and a Synchrotron Radiation (SR) type apparatus using synchrotron radiation. 
     SUMMARY 
     A laser apparatus according to an aspect of the present disclosure includes: a beam splitter configured to split a pulse laser beam into a first beam path and a second beam path; an optical sensor provided in the first beam path; an amplifier including an amplification region provided in the second beam path and being configured to amplify and emit the pulse laser beam incident thereon along the second beam path; a wavefront controller provided in the second beam path between the beam splitter and the amplifier; and a processor configured to receive an output signal from the optical sensor and transmit a control signal to the wavefront controller. 
     A laser apparatus according to another aspect of the present disclosure includes: a first beam splitter configured to split a pulse laser beam into a first beam path and a second beam path; a first optical sensor provided in the first beam path; an amplifier including an amplification region provided in the second beam path and being configured to amplify and emit the pulse laser beam incident thereon along the second beam path; a wavefront controller provided in the second beam path between the first beam splitter and the amplifier; a second beam splitter configured to split the pulse laser beam emitted from the amplifier into a third beam path and a fourth beam path; a second optical sensor provided in the third beam path; and a processor configured to receive an output signal from the first optical sensor and transmit a first control signal to the wavefront controller and, after that, receive an output signal from the second optical sensor and transmit a second control signal to the wavefront controller. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
       Hereinafter, various embodiments of the present disclosure will be described, as mere examples, with reference to the accompanying drawings. 
         FIG. 1  schematically illustrates a configuration of an exemplary LPP type EUV light generation system. 
         FIG. 2  is a partial sectional view illustrating a configuration of a laser apparatus according to a first embodiment of the present disclosure. 
         FIG. 3  is an enlarged view of one amplifier, one wavefront controller, one beam characteristics measurement unit, and one processor that are shown in  FIG. 2 . 
         FIGS. 4A and 4B  are diagrams for discussing a function of the wavefront controller. 
         FIG. 5  is an enlarged view of one wavefront controller and one amplifier. 
         FIG. 6  is an enlarged view of a beam waist measuring instrument. 
         FIG. 7  shows an example of a beam path in the amplifier prior to transmission of a control signal to the wavefront controller. 
         FIG. 8  is a flowchart showing an exemplary operation of the processor shown in  FIG. 3 . 
         FIG. 9  is a flowchart showing details of a process in step S 100  shown in  FIG. 8 . 
         FIG. 10  is a flowchart showing details of a process in step S 110  shown in  FIG. 9 . 
         FIG. 11  is a flowchart showing details of a process in step S 120  shown in  FIG. 9 . 
         FIG. 12  is a flowchart showing details of a process in step S 130  shown in  FIG. 9 . 
         FIG. 13  is a flowchart showing details of a process in step S 200  shown in  FIG. 8 . 
         FIG. 14  is a partial sectional view illustrating a configuration of a laser apparatus according to a second embodiment of the present disclosure. 
         FIG. 15  is an enlarged view of a downstream beam characteristics measurement unit and a processor, as well as one amplifier, one wavefront controller, one beam characteristics measurement unit, and one processor that are shown in  FIG. 14 . 
         FIG. 16  is a flowchart showing an exemplary operation of a processor shown in  FIG. 15 . 
         FIG. 17  is a flowchart showing details of a process in step S 400  shown in  FIG. 16 . 
         FIG. 18  is a flowchart showing details of a process in step S 600  shown in  FIG. 16 . 
         FIG. 19  is a flowchart showing an exemplary operation of a processor in a laser apparatus according to a third embodiment of the present disclosure. 
         FIG. 20A  is a flowchart showing details of a process in step S 50  shown in  FIG. 19 . 
         FIGS. 20B and 20C  are diagrams for discussing the process shown in  FIG. 20A . 
         FIG. 21  is a partial sectional view illustrating a configuration of a laser apparatus according to a fourth embodiment of the present disclosure. 
         FIG. 22A  is an internal transparent view illustrating a configuration of a triaxial orthogonal amplifier as a first example of an amplifier. 
         FIG. 22B  is a cross-sectional view taken along the line XXIIB-XXIIB in  FIG. 22A . 
         FIG. 23  is a perspective view illustrating a configuration of a high-speed axial-flow amplifier as a second example of the amplifier. 
         FIGS. 24A to 24C  are conceptual diagrams of a variable radius mirror as a first example of the wavefront controller. 
         FIG. 24D  is a partial sectional view illustrating a specific configuration of each of the variable radius mirrors shown in  FIGS. 24A to 24C . 
         FIG. 25  shows a second example of the wavefront controller. 
         FIG. 26A to 26C  illustrate a configuration of a third example of the wavefront controller. 
         FIG. 27  is a block diagram schematically illustrating an exemplary configuration of a processor. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, various embodiments of the present disclosure will be described in detail with reference to the drawings. The embodiments to be described below represent some examples of the present disclosure, and do not limit the scope of the present disclosure. Further, the configuration(s) and operation(s) described in each embodiment are not all essential as the configuration(s) and operation(s) of the present disclosure. Corresponding elements are referenced by corresponding reference symbols, and duplicate descriptions thereof will be omitted herein. 
     &lt;Contents&gt; 
     1. Overview 
     2. Overview of EUV Light Generation System 
     2.1 Configuration 
     2.2 Operation 
     3. Laser Apparatus Including Wavefront Controller (First Embodiment) 
     3.1 Overview of Configuration 
     3.2 Details of Configuration
         3.2.1 Amplifier   3.2.2 Wavefront Controller   3.2.3 Beam Characteristics Measurement Unit   3.2.4 Processor       

     3.3 Operation
         3.3.1 Main Flow   3.3.2 Calculation of Beam Characteristics
           3.3.2.1 Calculation of Win   3.3.2.2 Calculation of W 0m  and Zwm   3.3.2.3 Calculation of M 2  and Rin   
           3.3.3 Calculation of Target Value of Focal Power       

     3.4 Others 
     4. Laser Apparatus That Performs Beam Diameter Control (Second Embodiment) 
     4.1 Configuration 
     4.2 Operation
         4.2.1 Main Flow   4.2.2 Calculation of Win(k+1)   4.2.3 Setting of Target Value of Focal Power       

     4.3 Working Effects 
     5. Laser Apparatus That Determines Whether to Perform Beam Control (Third Embodiment) 
     5.1 Main Flow 
     5.2 Analysis of Beam Profile 
     6. Laser Apparatus That Performs Beam Control across a Plurality of Amplifiers (Fourth Embodiment) 
     7. Others 
     7.1 Examples of Amplifier
         7.1.1 First Example   7.1.2 Second Example       

     7.2 Examples of Wavefront Controller
         7.2.1 First Example   7.2.2 Second Example   7.2.3 Third Example       

     7.3 Configuration of Processor 
     1. OVERVIEW 
     In an LPP type EUV light generation system, a target material outputted into a chamber may be turned into plasma by being irradiated with a laser beam outputted from a laser apparatus. Then, light including EUV light may be emitted from the plasma. The emitted EUV light may be collected by an EUV collector mirror provided inside the chamber, and outputted to an external apparatus such as an exposure apparatus. 
     The laser apparatus may include an amplifier configured to amplify a pulse laser beam outputted from a master oscillator. However, a change in temperature of an optical element provided between the master oscillator and the amplifier may cause the optical element to deform and thus cause the wavefront of the pulse laser beam to fluctuate. The fluctuation of the wavefront of the pulse laser beam may sometimes cause the beam diameter of the pulse laser beam to be enlarged inside the amplifier. Moreover, a part of the pulse laser beam may be reflected by an electrode inside the amplifier or blocked by an element around an opening of the amplifier to have a beam profile that is different from the desired beam profile. 
     It is conceivable to provide a wavefront controller between the master oscillator and the amplifier and perform feedback control on the wavefront controller on the basis of the pulse laser beam that is outputted from the amplifier. However, reflection of a part of the pulse laser beam by the electrode inside the amplifier or blockage of a part of the pulse laser beam by the element around the opening of the amplifier may complicate the beam profile of the pulse laser beam that is outputted from the amplifier. The complicated beam profile may make it difficult to perform feedback control on the wavefront controller. 
     According to an aspect of the present disclosure, a wavefront controller may be provided in a beam path of the pulse laser beam upstream from the amplifier. A beam characteristics measurement unit including a beam splitter and an optical sensor may be provided in a beam path of the pulse laser beam further upstream from the wavefront controller. A processor may transmit a control signal to the wavefront controller in accordance with an output signal from the beam characteristics measurement unit. This makes it possible to measure the beam characteristics of the pulse laser beam near the wavefront controller, moreover, may prevent a part of the pulse laser beam from being undesirably reflected by the electrode inside the amplifier or being undesirably blocked by the element around the opening of the amplifier. 
     2. OVERVIEW OF EUV LIGHT GENERATION SYSTEM 
     2.1 Configuration 
       FIG. 1  schematically illustrates a configuration of an exemplary LPP type EUV light generation system. An EUV light generation apparatus  1  may be used with at least one laser apparatus  3 . In the present disclosure, a system that includes the EUV light generation apparatus  1  and the laser apparatus  3  may be referred to as an EUV light generation system  11 . As shown in  FIG. 1  and described in detail below, the EUV light generation apparatus  1  may include a chamber  2  and a target generation unit  26 . The chamber  2  may be sealed airtight. The target generation unit  26  may be mounted onto the chamber  2  to penetrate a wall of the chamber  2 . A target material to be outputted from the target generation unit  26  may include, but is not limited to, tin, terbium, gadolinium, lithium, xenon, or the combination of any two or more of them. 
     The chamber  2  may have at least one through-hole in its wall. A window  21  may be provided on the through-hole, and a pulse laser beam  32  outputted from the laser apparatus  3  may travel through the window  21 . An EUV collector mirror  23  having a spheroidal reflective surface, for example, may be provided in the chamber  2 . The EUV collector mirror  23  may have first and second focusing points. The EUV collector mirror  23  may have, on the surface thereof, a multi-layered reflective film in which molybdenum and silicon are alternately laminated, for example. The EUV collector mirror  23  may be preferably positioned such that the first focusing point lies in a plasma generation region  25  and the second focusing point lies in an intermediate focus (IF) region  292 . If necessary, the EUV collector mirror  23  may have a through-hole  24  at the center thereof, and a pulse laser beam  33  may travel through the through-hole  24 . 
     The EUV light generation apparatus  1  may include an EUV light generation controller  5 , a target sensor  4 , and the like. The target sensor  4  may have an imaging function and may be configured to detect the presence, the trajectory, the position, the speed, etc. of a target  27 . 
     The EUV light generation apparatus  1  may include a connection part  29  for allowing the interior of the chamber  2  to be in communication with the interior of the exposure apparatus  6 . A wall  291  having an aperture may be provided in the connection part  29 . The wall  291  may be positioned such that the aperture is positioned at the second focusing point of the EUV collector mirror  23 . 
     Further, the EUV light generation apparatus  1  may also include a laser beam direction control unit  34 , a laser beam focusing mirror  22 , a target collector  28  for collecting targets  27 , and the like. The laser beam direction control unit  34  may include an optical element for defining the travel direction of a pulse laser beam and an actuator for adjusting, the position and the posture of the optical element. 
     2.2 Operation 
     With continued reference to  FIG. 1 , a pulse laser beam  31  outputted from the laser apparatus  3  may pass through the laser beam direction control unit  34 , travel through the window  21  as the pulse laser beam  32 , and enter the chamber  2 . The pulse laser beam  32  may travel inside the chamber  2  along at least one laser beam path, be reflected by the laser beam focusing mirror  22 , and strike at least one target  27  as the pulse laser beam  33 . 
     The target generation unit  26  may be configured to output the target(s)  27  toward the plasma generation region  25  in the chamber  2 . The target  27  may be irradiated with at least one pulse of the pulse laser beam  33 . The target  27  having been irradiated with the pulse laser beam may be turned into plasma, and radiated light  251  may be emitted from the plasma. The EUV collector mirror  23  may reflect EUV light included in the radiated light  251  with higher reflectance as compared with light of other wavelength regions. Reflected light  252  including the EUV light, which is reflected by the EUV collector mirror  23 , may be focused on the intermediate focus region  292  and be outputted to the exposure apparatus  6 . Here, one target  27  may be irradiated with multiple pulses included in the pulse laser beam  33 . 
     The EUV light generation controller  5  may be configured to integrally control the whole EUV light generation system  11 . The EUV light generation controller  5  may be configured to process image data of the target  27  captured by the target sensor  4 , and the like. Further, the EUV light generation controller  5  may be configured to control the timing at which the target  27  is outputted, the direction into which the target  27  is outputted, and the like. Furthermore, the EUV light generation controller  5  may be configured to control the timing at which the laser apparatus  3  oscillates, the direction in which the pulse laser beam  32  travels, the position at which the pulse laser beam  33  is focused, and the like. The various controls mentioned above are merely examples, and other controls may be added as necessary. 
     3. LASER APPARATUS INCLUDING WAVEFRONT CONTROLLER (FIRST EMBODIMENT) 
     3.1 Overview of Configuration 
       FIG. 2  is a partial sectional view illustrating a configuration of a laser apparatus  3  according to a first embodiment of the present disclosure. The laser apparatus  3  may include a master oscillator MO and a plurality of amplifiers PA( 1 ), PA( 2 ), . . . , and PA(n). The master oscillator MO may output a pulse laser beam  30 , and the plurality of amplifiers PA( 1 ), PA( 2 ), . . . , and PA(n) may be provided in a beam path of the pulse laser beam  30  to amplify the pulse laser beam  30  in sequence. A relay optical system including high-reflection mirrors  35   a  and  35   b  and the like may be provided between the plurality of amplifiers PA( 1 ), PA( 2 ), . . . , and PA(n). 
     The number of amplifiers may be n. The following description assumes that n is an integer of 2 or greater. Note, however, that n may be 1. Further, in the following description, any one of the plurality of amplifiers PA( 1 ), PA( 2 ), . . . , and PA(n), excluding the final-stage amplifier PA(n), may be represented by PA(k). The amplifier of the stage following the amplifier PA(k) may be represented by PA (k+1). 
     A wavefront controller  50 ( k ) may be provided in a beam path of the pulse laser beam  30  upstream from the amplifier PA(k). A beam characteristics measurement unit  40 ( k ) may be provided further upstream from the wavefront controller  50 ( k ). A processor  60 ( k ) may transmit a control signal to the wavefront controller  50 ( k ) on the basis of data outputted from the beam characteristics measurement unit  40 ( k ). A wavefront controller  50 ( n ) and a beam characteristics measurement unit  40 ( n ) may be provided upstream from the final-stage amplifier PA(n). A processor  60 ( n ) may transmit a control signal to the wavefront controller  50 ( n ) on the basis of data outputted from the beam characteristics measurement unit  40 ( n ). 
     Note, however, that a wavefront controller or a beam characteristics measurement unit does not need to be provided upstream from the first-stage amplifier PA( 1 ) or upstream from the second-stage amplifier PA( 2 ). The pulse laser beam  30  may have smaller energy upstream from the first-stage amplifier PA( 1 ) or upstream from the second-stage amplifier PA( 2 ) than it does downstream therefrom. In a case where the pulse laser beam  30  has small energy, deformation of an optical element due to heating of the optical element may not tend to occur. This may decrease the need for wavefront adjustment by the present disclosure. 
     A pulse laser beam outputted from the final-stage amplifier PA(n) may enter the laser beam direction control unit  34   a  as a pulse laser beam  31 . A pulse laser beam  32  having exited from the laser beam direction control unit  34   a  may enter the chamber  2 . 
     3.2 Details of Configuration 
       FIG. 3  is an enlarged view of one amplifier PA(k), one wavefront controller  50 ( k ), one beam characteristics measurement unit  40 ( k ), and one processor  60 ( k ) that are shown in  FIG. 2 . Each of  FIGS. 4A and 4B  is a diagram for discussing a function of the wavefront controller  50 ( k ).  FIG. 5  is an enlarged view of one wavefront controller  50 ( k ) and one amplifier PA(k). 
     3.2.1 Amplifier 
     The amplifier PA(k) may include a laser chamber  70  and a pair of electrodes  71  and  72 . A laser gas containing a CO 2  gas may be enclosed in the laser chamber  70 . A high-frequency power supply (not shown) may apply a high voltage between the electrodes  71  and  72  to generate discharge that excites the laser gas to form an amplification region  73  between the electrodes  71  and  72 . When the pulse laser beam  30  enters through an entrance window  74  to the laser chamber  70 , the pulse laser beam  30  may be amplified and outputted through an exit window  75 . 
     3.2.2 Wavefront Controller 
     As shown in  FIG. 4A , the wavefront controller  50 ( k ) may convert a pulse laser beam having a planar wavefront into a pulse laser beam having a concave wavefront. As shown in  FIG. 4B , the wavefront controller  50 ( k ) may convert a pulse laser beam having a planar wavefront into a pulse laser beam having a convex wavefront. 
     That is, the wavefront controller  50 ( k ) may be an optical element that is capable of converting a wavefront of a pulse laser beam as shown in  FIG. 4A  or as shown in  FIG. 4B . Further, the wavefront controller  50 ( k ) may be capable of converting a wavefront having a given curvature in a given range into a wavefront having another given curvature in the given range. 
     When the wavefront controller  50 ( k ) is controlled to have a focal length F, the focal power Pw of the wavefront controller  50 ( k ) may be expressed in the following expression.
 
 Pw= 1/ F  
 
     When F is a positive value, a pulse laser beam having a planar wavefront may be converted into a pulse laser beam having a concave wavefront that is focused at a point distanced by the focal length F, in the forward direction, from the principal point of the wavefront controller  50 ( k ) (see  FIG. 4A ). 
     When F is a negative value, a pulse laser beam having a planar wavefront may be converted into a pulse laser beam having a convex wavefront that is equivalent to a wavefront of a light generated from a virtual point light source at a position distanced by the focal length F, in the backward direction, from the principal point of the wavefront controller  50 ( k ) (see  FIG. 4B ). 
     3.2.3 Beam Characteristics Measurement Unit 
     The description follows with continued reference to  FIG. 3 . 
     The beam characteristics measurement unit  40 ( k ) may include a beam splitter  41 , a beam splitter  42 , a beam profile measuring instrument  43 , and a beam waist measuring instrument  46 . 
     The beam splitter  41  may reflect a part of the pulse laser beam  30  and transmit the remaining part of the pulse laser beam  30  with high transmittance. By doing so, the beam splitter  41  may split the pulse laser beam  30  into a first beam path B 1  through which reflected light passes and a second beam path B 2  through which transmitted light passes. The wavefront controller  50 ( k ) and the amplifier PA(k) may be provided in the second beam path B 2 . The beam splitter  41  may correspond to the first beam splitter of the present disclosure. 
     The beam splitter  42 , provided in the first beam path B 1 , may transmit a part of a pulse laser beam toward the beam profile measuring instrument  43  and reflect the remaining part toward the beam waist measuring instrument  46 . 
     The beam profile measuring instrument  43  may include a transfer optical system  44  and an optical sensor  45 . The transfer optical system  44  may transfer a beam cross-sectional image at a predetermined position P 1  on a beam path of the pulse laser beam onto the photosensitive surface of the optical sensor  45 . The optical sensor  45  may be an image sensor. The optical sensor  45  may output data of a beam intensity distribution of the pulse laser beam at the predetermined position P 1  as an output signal to the processor  60 ( k ). A distance L 1  along the second beam path B 2  from the beam splitter  41  to the wavefront controller  50 ( k ) and a distance L 2  along the first beam path B 1  from the beam splitter  41  to the predetermined position P 1  may be substantially equal. The optical sensor  45  may correspond to the first optical sensor of the present disclosure. 
     The beam waist measuring instrument  46  may include a focusing optical system  47 , an optical sensor  48 , and a uniaxial stage  49 . 
       FIG. 6  is an enlarged view of the beam waist measuring instrument  46 . Note, however, that  FIG. 6  shows a left-right reversal of the beam waist measuring instrument  46  shown in  FIG. 3 . 
     The focusing optical system  47  may focus a pulse laser beam. In accordance with a control signal that is outputted from the processor  60 ( k ), the uniaxial stage  49  may move the optical sensor  48  along a beam axis of the pulse laser beam that is focused by the focusing optical system  47 . The optical sensor  48  may be an image sensor. The optical sensor  48  may output data of a beam intensity distribution of the pulse laser beam at multiple positions to which the optical sensor  48  is moved by the uniaxial stage  49  as an output signal to the processor  60 ( k ). The distance L 1  along the second beam path B 2  from the beam splitter  41  to the wavefront controller  50 ( k ) and a distance L 3  along the first beam path B 1  from the beam splitter  41  to the focusing optical system  47  may be substantially equal. The optical sensor  48  may correspond to the first optical sensor of the present disclosure. 
     3.2.4 Processor 
     The processor  60 ( k ) may calculate the beam radius Win of the pulse laser beam at the predetermined position P 1  on the basis of the data of the beam intensity distribution received from the beam profile measuring instrument  43 . Since the above-described distances L 1  and L 2  are substantially equal, the beam radius Win of the pulse laser beam at the predetermined position P 1  may be treated as being equal to the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ).  FIG. 5  shows the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     On the basis of the data of the beam intensity distribution at the multiple positions received from the beam waist measuring instrument  46 , the processor  60 ( k ) may calculate the beam waist radius W 0m  and beam waist position Zwm of the pulse laser beam that is focused by the focusing optical system  47 . The beam waist position Zwm may be a distance along a beam axis to the position of a beam waist based on the position of the focusing optical system  47 .  FIG. 6  shows the beam waist radius W 0m  and the beam waist position Zwm. 
     The processor  60 ( k ) may calculate the curvature radius Rin of the wavefront of the pulse laser beam incident on the focusing optical system  47  and the M square value M 2  of the pulse laser beam incident on the focusing optical system  47  on the basis of the beam waist radius W 0m , the beam waist position Zwm, and the beam radius Win of the pulse laser beam incident on the focusing optical system  47 .  FIG. 6  shows the beam radius Win of the pulse laser beam incident on the focusing optical system  47  and the curvature radius Rin of the wavefront of the pulse laser beam incident on the focusing optical system  47 . Since the above-described distances L 1  and L 3  are substantially equal, the value of the beam radius Win (see  FIG. 5 ) of the pulse laser beam incident on the wavefront controller  50 ( k ) may be used as the beam radius Win of the pulse laser beam incident on the focusing optical system  47 . 
     Since the above-described distances L 1  and L 3  are substantially equal, the M square value M 2  of the pulse laser beam incident on the focusing optical system  47  and the curvature radius Rin of the wavefront of the pulse laser beam incident on the focusing optical system  47  may be treated as being equal to the M square value M 2  of the pulse laser beam incident on the wavefront controller  50 ( k ) and the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ).  FIG. 5  shows the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     The processor  60 ( k ) may calculate a target value Pwt of the focal power of the wavefront controller  50 ( k ) on the basis of the following values calculated on the basis of the data received from the beam characteristics measurement unit  40 ( k ) as described above: 
     Win: Beam radius of the pulse laser beam incident on the wavefront controller  50 ( k ). It should be noted that the beam radius refers to the radius of a region having beam intensity equal to or greater than 1/e 2  of the peak value of beam intensity in a beam intensity distribution. 
     M 2 : M square value that represents the focusing performance of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     Rin: Curvature radius of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ). It should be noted that the curvature radius of the wavefront takes on a positive value in a case where the front side of the wavefront has a concave surface and takes on a negative value in a case where the front side of the wavefront has a convex surface. 
     The target value Pwt of the focal power may be calculated as such a value that the pulse laser beam  30  reduces the maximum value of its beam diameter between first and second positions positioned with the amplification region  73  of the amplifier PA(k) interposed therebetween. To calculate the target value Pwt of the focal power, the following known values concerning the dimensions of the amplifier PA(k) may be used: 
     Zin: Distance from the wavefront controller  50 ( k ) to an entrance end of the pair of electrodes  71  and  72 . 
     Din: Distance between the electrodes  71  and  72  at the entrance end. 
     Zout: Distance from the wavefront controller  50 ( k ) to an exit end of the pair of electrodes  71  and  72 . 
     Dout: Distance between the electrodes  71  and  72  at the exit end. 
     These known values may be stored in the after-mentioned storage memory. 
       FIG. 5  shows Zin, Din, Zout, and Dout, as well as the above-described Win and Rin. 
     Assuming the first position is a position where Z=Zin, it is desirable that the beam diameter at the first position be smaller than Din. Assuming the second position is a position where Z=Zout, it is desirable that the beam diameter at the second position be smaller than Dout. 
     In  FIG. 5 , furthermore, the following parameters may be defined: 
     Zw: Distance from the wavefront controller  50 ( k ) to the beam waist of the pulse laser beam. This distance Zw may vary depending on the focal power of the wavefront controller  50 ( k ), the beam characteristics of the pulse laser beam, and the like. 
     W 0 : Radius of the beam waist of the pulse laser beam. The radius W 0  of the beam waist may vary depending on the focal power of the wavefront controller  50 ( k ), the beam characteristics of the pulse laser beam, and the like. 
     Zt: Position vector of a given position along the beam axis of the pulse laser beam from the position of the beam waist of the pulse laser beam outputted from the wavefront controller  50 ( k ). Zt is positive in the travel direction of the pulse laser beam. The distance from the wavefront controller  50 ( k ) to the beam waist is Zw, which is expressed in Zt=Z−Zw. For example, the wavefront controller  50 ( k ) may be said to be at a position where Z=0, i.e., a position where Zt=−Zw. 
     W(Zt): Beam radius of the pulse laser beam at the given position Zt. 
     R(Zt): Curvature radius of the wavefront of the pulse laser beam at the given position Zt. 
     In general, the beam radius W(Zt) and the curvature radius R(Zt) of the wavefront are expressed in the following expressions: 
     
       
         
           
             
               
                 
                   
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     In these expressions, λ may be the wavelength of the pulse laser beam. The beam intensity distribution of the pulse laser beam may be a Gaussian distribution. λ may be stored in the after-mentioned storage memory. 
     The processor  60 ( k ) may transmit a control signal to the wavefront controller  50 ( k ) so that the focal power of the wavefront controller  50 ( k ) takes on the target value Pwt thus calculated. 
       FIG. 7  shows an example of a beam path in the amplifier PA(k) prior to transmission of a control signal to the wavefront controller  50 ( k ). As shown in  FIG. 7 , a part of the pulse laser beam  30  incident on the amplifier PA(k) may strike the vicinity of the exit end of the pair of electrodes  71  and  72 . Such a part of the pulse laser beam  30  may be reflected by the pair of electrodes  71  and  72  to complicate the beam profile. The processor  60 ( k ) may transmit a control signal to the wavefront controller  50 ( k ) so that the beam diameter at the position where Z=Zin is smaller than Din and the beam diameter at the position where Z=Zout is smaller than Dout. 
     3.3 Operation 
     3.3.1 Main Flow 
       FIG. 8  is a flowchart showing an exemplary operation of the processor  60 ( k ) shown in  FIG. 3 . The processor  60 ( k ) may control the wavefront controller  50 ( k ) through the following process. The process shown in  FIG. 8  may be executed at regular time intervals during operation of the EUV light generation system  11  (see  FIG. 1 ). 
     First, in step S 100 , the processor  60 ( k ) may calculate the beam radius Win and M square value M 2  of a pulse laser beam incident on the wavefront controller  50 ( k ) and the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ) on the basis of data outputted from the beam characteristics measurement unit  40 ( k ). Details of this process will be described below with reference to  FIGS. 9 to 12 . 
     Next, in step S 200 , the processor  60 ( k ) may calculate the target value Pwt of the focal power of the wavefront controller  50 ( k ) on the basis of the beam radius Win and M square value M 2  of the pulse laser beam incident on the wavefront controller  50 ( k ) and the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ). Details of this process will be described below with reference to  FIG. 13 . 
     Next, in step S 300 , the processor  60 ( k ) may transmit a control signal to the wavefront controller  50 ( k ) so that the focal power takes on the target value Pwt. 
     Upon completion of the processing in step S 300 , the processor  60 ( k ) may end the process of the present flowchart. 
     3.3.2 Calculation of Beam Characteristics 
       FIG. 9  is a flowchart showing details of a process in step S 100  shown in  FIG. 8 . The process shown in  FIG. 9  may be performed by the processor  60 ( k ) as a subroutine of step S 100 . The processor  60 ( k ) may calculate Win, M 2 , and Rin through the following process. 
     First, in step S 110 , the processor  60 ( k ) may calculate the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ) on the basis of data outputted from the beam profile measuring instrument  43 . Details of this process will be described below with reference to  FIG. 10 . 
     Next, in step S 120 , the processor  60 ( k ) may calculate the beam waist radius W 0m  and beam waist position Zwm on the basis of data outputted from the beam waist measuring instrument  46 . Details of this process will be described below with reference to  FIG. 11 . 
     Next, in step S 130 , the processor (k) may calculate the M square value M 2  of the pulse laser beam incident on the wavefront controller  50 ( k ) and the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ) on the basis of the beam radius Win, the beam waist radius W 0m , and the beam waist position Zwm. Details of this process will be described below with reference to  FIG. 12 . 
     Upon completion of the processing in step S 130 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 200  shown in  FIG. 8 . 
     3.3.2.1 Calculation of Win 
       FIG. 10  is a flowchart showing details of a process in step S 110  shown in  FIG. 9 . The process shown in  FIG. 10  may be performed by the processor  60 ( k ) as a subroutine of step S 110 . The processor  60 ( k ) may calculate the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ) through the following process. 
     First, in step S 111 , the processor  60 ( k ) may read out the data of the beam intensity distribution outputted from the beam profile measuring instrument  43 . 
     Next, in step S 112 , the processor  60 ( k ) may calculate the diameter D of a region having beam intensity equal to or greater than 1/e 2  of the peak value in the beam intensity distribution thus read out. Note here that e may be a Napier&#39;s constant. 
     Next, in step S 113 , the processor  60 ( k ) may calculate the beam radius Win using a magnification Ma of the transfer optical system  44 . The beam radius Win may be calculated by the following expression:
 
 W in=(½)·( D/Ma )
 
     This beam radius Win may be treated as being equal to the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     Upon completion of the processing in step S 113 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 120  shown in  FIGS. 9 and 11 . 
     3.3.2.2 Calculation of Wa, and Zwm 
       FIG. 11  is a flowchart showing details of a process in step S 120  shown in  FIG. 9 . The process shown in  FIG. 11  may be performed by the processor  60 ( k ) as a subroutine of step S 120 . The processor  60 ( k ) may calculate the beam waist radius W 0m  and beam waist position Zwm of the pulse laser beam that is focused by the focusing optical system  47  through the following process (see  FIG. 6 ). 
     First, in step S 121 , the processor  60 ( k ) may set an initial value of a position Z of the photosensitive surface of the optical sensor  48  and an initial value of a beam diameter D f0  on the photosensitive surface of the optical sensor  48  as follows, respectively:
 
 Z=Z   0  
 
 D   f0 =2 W in
 
     Note here that Z 0  may be a distance from the position of the focusing optical system  47  to the photosensitive surface of the optical sensor  48  at the time when the optical sensor  48  has been brought closest to the focusing optical system  47  by the uniaxial stage  49 . 
     Further, Win is the beam radius of the pulse laser beam incident on the focusing optical system  47 , and as Win, the value of the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ) as calculated by the process shown in  FIG. 10  may be used. 
     Next, in step S 122 , the processor  60 ( k ) may transmit a control signal to the uniaxial stage  49  so that the position of the photosensitive surface of the optical sensor  48  of the beam waist measuring instrument  46  becomes the set position Z. 
     Next, in step S 123 , the processor  60 ( k ) may read out the data of the beam intensity distribution outputted from the optical sensor  48  of the beam waist measuring instrument  46 . 
     Next, in step S 124 , the processor  60 ( k ) may calculate the diameter D f  of a region having beam intensity equal to or greater than 1/e 2  of the peak value in the beam intensity distribution thus read out. 
     Next, in step S 125 , the processor  60 ( k ) may compare the diameter D f0  with the newly calculated diameter D f . If the newly calculated diameter D f  is smaller than the diameter D f0  (S 125 ; NO), the processor  60 ( k ) may proceed to step S 126 . 
     In step S 126 , the processor  60 ( k ) may update the value of the diameter D f0  to the value of the newly calculated diameter D f . 
     Next, in step S 127 , the processor  60 ( k ) may update the position Z of the photosensitive surface of the optical sensor  48  by adding a positive number ΔZ to the value of S. 
     After step S 127 , the processor  60 ( k ) may return to the above-described step S 122  and repeat the processing from  8122  to  8125 . 
     If, in step S 125 , the newly calculated diameter D f  is equal to or greater than the diameter D f0  (S 125 ; YES), it can be deemed that the beam diameter on the photosensitive surface of the optical sensor  48  has reached the local minimal value. Then, the processor  60 ( k ) may proceed to step S 128 . 
     In step S 128 , the processor  60 ( k ) may store the value of the position Z of the photosensitive surface of the optical sensor  48  as the beam waist position Zwm in the after-mentioned memory. 
     Next, in step S 129 , the processor  60 ( k ) may store half the value of the newly calculated diameter D f  as the beam waist radius W 0m  in the after-mentioned memory. 
     Upon completion of the processing in step S 129 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 130  shown in  FIGS. 9 and 12 . 
     It is possible to, without being limited to the process method of the present flowchart, measure beam diameters D f  at multiple positions Z and, on the basis of these values of Z and D f , derive an approximate curve that indicates a relationship between Z and D f . It is possible to calculate the beam waist radius W 0m  and the beam waist position Zwm by obtaining the local minimal value of D f  and Z at which D f  takes on the local minimal value. 
     3.3.2.3 Calculation of M 2  and Rin 
       FIG. 12  is a flowchart showing details of a process in step S 130  shown in  FIG. 9 . The process shown in  FIG. 12  may be performed by the processor  60 ( k ) as a subroutine of step S 130 . The processor  60 ( k ) may calculate the M square value M 2  of the pulse laser beam incident on the wavefront controller  50 ( k ) and the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ) through the following process. 
     First, in step S 131 , the processor  60 ( k ) may set an initial value of the M square value M 2  of the pulse laser beam incident on the focusing optical system  47  to 1. 
     Next, in step S 132 , the processor  60 ( k ) may calculate the beam radius calculated value Wine of the pulse laser beam incident on the focusing optical system  47  from the M square value M 2 , the beam waist radius W 0m , and the beam waist position Zwm. In Expression 1 above, Zt may be a position vector, based on the beam waist position, which is positive in the travel direction of the pulse laser beam. Since the beam waist position is Z=Zwm and the position of the focusing optical system  47  is Z=0, the position of the focusing optical system  47  based on the beam waist position may be Zt=−Zwm. Therefore, in Expression 1 above, the value of −Zwm may be substituted in Zt. In W 0  in Expression 1 above, the beam waist radius W 0m  may be substituted. The beam radius calculated value Wine of the pulse laser beam incident on the focusing optical system  47  may be calculated as follows: 
     
       
         
           
             
               
                 
                   Winc 
                   = 
                   
                     
                       
                         W 
                         
                           0 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           m 
                         
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     - 
                                     1 
                                   
                                   × 
                                   
                                     ( 
                                     
                                       - 
                                       Zwm 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     w 
                                     
                                       0 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       m 
                                     
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                     
                       1 
                       / 
                       2 
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     Next, in step S 133 , the processor  60 ( k ) may determine whether a difference between the beam radius calculated value Winc and the beam radius Win of the pulse laser beam incident on the focusing optical system  47  falls within an allowable range. For example, the processor  60 ( k ) may determine whether the following condition is satisfied:
 
|( W in− W in c )/ W in|≦Err w in
 
     Note here that Errwin may be a value that is set as an allowed value of an error. As the beam radius Win of the pulse laser beam incident on the focusing optical system  47 , the beam radius Win calculated by the process shown in  FIG. 10  may be used. 
     If the difference between Winc and Win does not fall within the allowable range (S 133 ; NO), it may be said the value set as the M square value M 2  was not appropriate. Therefore, in step S 134 , the processor  60 ( k ) may update the value of M 2  by adding a positive number ΔM to the value of M 2 . After step S 134 , the processor  60 ( k ) may return to step S 132  and repeat the processing from  8132  to  8133 . 
     If the difference between Winc and Win falls within the allowable range (S 133 ; YES), it may be deemed that the value set as the M square value M 2  was appropriate. Therefore, the processor  60 ( k ) may proceed to step S 135 . At this point in time, the M square value M 2  of the pulse laser beam incident on the focusing optical system  47  may be stored in the after-mentioned memory. The M square value M 2  of the pulse laser beam incident on the focusing optical system  47  may be treated as being equal to the N square value M 2  of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     In step S 135 , the processor  60 ( k ) may calculate the curvature radius Rf of the wavefront of a pulse laser beam exiting from the focusing optical system  47 . In Expression 2 above, St may be a position vector, based on the beam waist position, which is positive in the travel direction of the pulse laser beam. Since the beam waist position is Z=Zwm and the position of the focusing optical system  47  is Z=0, the position of the focusing optical system  47  based on the beam waist position may be Zt=−Zwm. Therefore, in Expression 2 above, the value of −Zwm may be substituted in St. In W 0  in Expression 2 above, the beam waist radius W 0m  may be substituted. The curvature radius Rf of the wavefront of the pulse laser beam exiting from the focusing optical system  47  may be calculated as follows: 
     
       
         
           
             
               
                 
                   Rf 
                   = 
                   
                     
                       - 
                       1 
                     
                     × 
                     
                       
                         ( 
                         
                           - 
                           Zwm 
                         
                         ) 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     w 
                                     
                                       0 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       m 
                                     
                                     2 
                                   
                                 
                                 
                                   
                                     - 
                                     1 
                                   
                                   × 
                                   
                                     ( 
                                     
                                       - 
                                       Zwm 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     Next, in step S 136 , the processor  60 ( k ) may calculate the curvature radius Rin of the wavefront of the pulse laser beam incident on the focusing optical system  47 . Since the curvature radius of the wavefront of the pulse laser beam exiting from the focusing optical system  47  is Rf, the focal power Pw of the focusing optical system  47  is expressed as follows:
 
 Pw= 1/ F= 1/ Rf− 1/ R in
 
     Therefore, the curvature radius Rin of the wavefront of the pulse laser beam incident on the focusing optical system  47  may be obtained as follows:
 
 R in= F·Rf /( F−Rf )
 
     This curvature radius Rin may be treated as being equal to the curvature radius Rin of the wavefront of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     Upon completion of the processing in step S 136 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 200  shown in  FIGS. 8 and 13 . 
     3.3.3 Calculation of Target Value of Focal Power 
       FIG. 13  is a flowchart showing details of a process in step S 200  shown in  FIG. 8 . The process shown in  FIG. 13  may be performed by the processor  60 ( k ) as a subroutine of step S 200 . The processor  60 ( k ) may calculate the target value Pwt of the focal power of the wavefront controller  50 ( k ) through the following process. 
     First, in step S 201 , the processor  60 ( k ) may set an initial value of the beam waist position Zw of a pulse laser beam outputted from the wavefront controller  50 ( k ) to Zin. Zin may be a distance from the wavefront controller  50 ( k ) to the entrance end of the pair of electrodes  71  and  72  (see  FIG. 5 ). 
     Next, in step S 202 , the processor  60 ( k ) may set an initial value of the beam waist radius W 0  of the pulse laser beam outputted from the wavefront controller  50 ( k ) to Win. Win may be the beam radius of the pulse laser beam incident on the wavefront controller  50 ( k ). 
     Next, in step S 203 , the processor  60 ( k ) may calculate the beam radius calculated value Wind of the pulse laser beam incident on the wavefront controller  50 ( k ). In Expression 1 above, Zt may be a position vector, based on the beam waist position, which is positive in the travel direction of the pulse laser beam. Since the beam waist position is Z=Zw and the position of the wavefront controller  50 ( k ) is Z=0, the position of the wavefront controller  50 ( k ) based on the beam waist position may be Zt=−Zw. Therefore, in Expression 1 above, −Zw may be substituted in Zt. The beam radius calculated value Wind of the pulse laser beam incident on the wavefront controller  50 ( k ) may be calculated as follows: 
     
       
         
           
             
               
                 
                   Wind 
                   = 
                   
                     
                       
                         W 
                         0 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     - 
                                     1 
                                   
                                   × 
                                   
                                     ( 
                                     
                                       - 
                                       Zw 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     W 
                                     0 
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                     
                       1 
                       / 
                       2 
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   5 
                 
               
             
           
         
       
     
     Next, in step S 204 , the processor  60 ( k ) may determine whether a difference between the beam radius calculated value Wind and the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ) falls within an allowable range. For example, the processor  60 ( k ) may determine whether the following condition is satisfied:
 
|( W in− W in d )/ W in|≦Err w in
 
     Note here that Errwin may be a value that is set as an allowed value of an error. As the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ), the beam radius Win calculated by the process shown in  FIG. 10  may be used. 
     If the difference between Wind and Win does not fall within the allowable range (S 204 ; NO), it may be said the value set as the value of the beam waist radius W 0  was not appropriate under the set beam waist position Zw. Therefore, in step S 205 , the processor  60 ( k ) may update the value of W 0  by subtracting a positive number ΔW 0  from the value of W 0 . After step S 205 , the processor  60 ( k ) may return to step S 203  and repeat the processing from S 203  to S 204 . 
     If the difference between Wind and Win falls within the allowable range (S 204 ; YES), it may be deemed that the value of the set beam waist radius W 0  was appropriate under the set beam waist position Zw. Therefore, the processor  60 ( k ) may proceed to step S 206 . 
     In step S 206 , the processor  60 ( k ) may determine whether the set beam waist position Zw is equal to or smaller than Zout. Zout may be a distance from the wavefront controller  50 ( k ) to the exit end of the pair of electrodes  71  and  72  (see  FIG. 5 ). If the set beam waist position Zw is equal to or smaller than Zout (S 206 ; YES), the processor  60 ( k ) may proceed to step S 207 . 
     In step S 207 , the processor  60 ( k ) may compare the beam diameters at the positions of Zin and Zout with the respective thresholds. In Expression 1 above, Zt may be a position vector, based on the beam waist position, which is positive in the travel direction of the pulse laser beam. Since the beam waist position is Z=Zw, the position of Zin based on the beam waist position may be Zt=Zin−Zw. Therefore, in Expression 1, (Zin−Zw) may be substituted in Zt. It is desirable that the beam radius at the position of Sin thus calculated be smaller than Din/2a, where Din is the distance between the electrodes  71  and  72  at the entrance end. Therefore, the following condition may be determined: 
     
       
         
           
             
               
                 
                   
                     Din 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       a 
                     
                   
                   &gt; 
                   
                     
                       
                         W 
                         0 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     ( 
                                     
                                       Zin 
                                       - 
                                       Zw 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     W 
                                     0 
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                     
                       1 
                       / 
                       2 
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   6 
                 
               
             
           
         
       
     
     Further, the position of Zout based on the beam waist position may be Zt=Zout−Zw. Therefore, in Expression 1, (Zout−Zw) may be substituted in Zt. It is desirable that the beam radius at the position of Zout thus calculated be smaller than Dout/2a, where Dout is the distance between the electrodes  71  and  72  at the exit end. Therefore, the following condition may be determined: 
     
       
         
           
             
               
                 
                   
                     Dout 
                     
                       2 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       a 
                     
                   
                   &gt; 
                   
                     
                       
                         W 
                         0 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   
                                     ( 
                                     
                                       Zout 
                                       - 
                                       Zw 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     W 
                                     0 
                                     2 
                                   
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                     
                       1 
                       / 
                       2 
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   7 
                 
               
             
           
         
       
     
     Note here that a may be a constant of not smaller than 1 to not greater than 3, preferably not smaller than 1.5 to not greater than 1.9, more preferably not smaller than 1.6 to not greater than 1.8. In a case where a is not smaller than 1, the pair of electrodes  71  and  72  may be prevented from being struck by a region having beam intensity equal to or greater than 1/e 2  of the peak value in a beam intensity distribution of the pulse laser beam. 
     If either Expression 6 or Expression 7 is not satisfied (S 207 ; NO), it may be said that the value of the beam waist position Zw was not appropriate. Therefore, in step S 208 , the processor  60 ( k ) may update the value of Zw by adding the positive number ΔZ to the value of Zw. After step S 208 , the processor  60 ( k ) may return to step S 202  and repeat the processing from S 202  to S 207 . 
     If both Expression 6 and Expression 7 are satisfied (S 207 ; YES), it may be deemed that the value of the beam waist position Zw was appropriate. Therefore, the processor  60 ( k ) may proceed to step S 210 . 
     If, in the above-described step S 206 , the set beam waist position Zw is not equal to or smaller than Zout (S 206 ; NO), the condition for step S 207  described above may not be satisfied even with a change in the beam waist position Zw from Zin to Zout. Therefore, the processor  60 ( k ) may proceed to step S 209 . 
     In step S 209 , the processor  60 ( k ) may transmit, to the EUV light generation controller  5 , a signal indicating that wavefront adjustment was impossible, and may end the process of the present flowchart. 
     In step S 210 , the processor  60 ( k ) may store the value of the set beam waist position Zw as the target beam waist position Zwt in the after-mentioned memory. 
     Next, in step S 211 , the processor  60 ( k ) may calculate the curvature radius Rout of the wavefront of a pulse laser beam exiting from the wavefront controller  50 ( k ). In Expression 2 above, Et may be a position vector, based on the beam waist position, which is positive in the travel direction of the pulse laser beam. Since the beam waist position is Z=Zwt and the position of the wavefront controller  50 ( k ) is Z=0, the position of the wavefront controller  50 ( k ) based on the beam waist position may be Zt=−Zwt. Therefore, in Expression 2 above, the value of −Zwt may be substituted in Zt. The curvature radius Rout of the wavefront of the pulse laser beam exiting from the wavefront controller  50 ( k ) may be calculated as follows: 
     
       
         
           
             
               
                 
                   Rout 
                   = 
                   
                     
                       - 
                       1 
                     
                     × 
                     
                       
                         ( 
                         
                           - 
                           Zwt 
                         
                         ) 
                       
                       ⁡ 
                       
                         [ 
                         
                           1 
                           + 
                           
                             
                               ( 
                               
                                 
                                   π 
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     W 
                                     0 
                                     2 
                                   
                                 
                                 
                                   
                                     - 
                                     1 
                                   
                                   × 
                                   
                                     ( 
                                     
                                       - 
                                       Zwt 
                                     
                                     ) 
                                   
                                   ⁢ 
                                   
                                     M 
                                     2 
                                   
                                   ⁢ 
                                   λ 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   Expression 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   8 
                 
               
             
           
         
       
     
     Next, in step S 212 , the processor  60 ( k ) may calculate the target value Pwt of the focal power of the wavefront controller  50 ( k ) through the following expression:
 
 Pwt= 1 /R out−1 /R in
 
     Upon completion of the processing in step S 212 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 300  shown in  FIG. 8 . 
     In this way, the target value Pwt of the focal power of the wavefront controller  50 ( k ) may be calculated, and a control signal may be transmitted to the wavefront controller  50 ( k ). 
     3.4 Others 
     The foregoing description assumes that the positions of the entrance end and exit end of the pair of electrodes  71  and  72  are the first and second positions, respectively. However, the present disclosure is not limited to this assumption. In a case where a plurality of apertures that allow passage of a pulse laser beam are provided inside an amplifier, the positions of these apertures may be the first and second positions. 
     The foregoing description has discussed a case where the distance L 1  and the distance L 2  are substantially equal and the distance L 1  and the distance L 3  are substantially equal. However, the present disclosure is not limited to this case. For example, a correction calculation based on the difference between the distance L 1  and the distance L 2  or L 3  may be possible, provided the distance L 2  and the distance L 3  are substantially equal and the beam radius and the curvature radius of the wavefront at a specific position on the beam path of a pulse laser beam can be calculated. Further, for example, the curvature radius of the wavefront can be correctively calculated on the basis of the difference between the distance L 1  and the distance L 3 , provided the distance L 1  and the distance L 2  are substantially equal and the beam radius Win of the pulse laser beam incident on the wavefront controller  50 ( k ) can be calculated. 
     4. LASER APPARATUS THAT PERFORMS BEAM DIAMETER CONTROL (SECOND EMBODIMENT) 
     4.1 Configuration 
       FIG. 14  is a partial sectional view illustrating a configuration of a laser apparatus  3  according to a second embodiment of the present disclosure.  FIG. 14  illustrates a beam characteristics measurement unit  40 ( n −1), a wavefront controller  50 ( n −1), a processor  60 ( n −1), and an amplifier PA(n−1) as examples of the beam characteristics measurement unit  40 ( k ), the wavefront controller  50 ( k ), the processor  60 ( k ), and the amplifier PA(k). The second embodiment is the same as the first embodiment in that the processor  60 ( n −1) controls the wavefront controller  50 ( n −1) on the basis of data outputted from the beam characteristics measurement unit  40 ( n −1). In the second embodiment, furthermore, the processor  60 ( n −1) may be configured to control the wavefront controller  50 ( n −1) on the basis of data outputted from a beam characteristics measurement unit  40 ( n ) on a downstream side of the amplifier PA(n−1). That is, the data outputted from the beam characteristics measurement unit  40 ( n ) may be not only used for controlling the wavefront controller  50 ( n ) but also used for controlling the upstream wavefront controller  50 ( n −1). On a downstream side of the amplifier PA(n), a beam characteristics measurement unit  40 ( n +1) may be further provided. 
       FIG. 15  is an enlarged view of a part of the laser apparatus  3  according to the second embodiment of the present disclosure. The beam characteristics measurement unit  40 ( k ), the wavefront controller  50 ( k ), the processor  60 ( k ), and the amplifier PA(k) in  FIG. 15  may correspond to the beam characteristics measurement unit  40 ( n −1), the wavefront controller  50 ( n −1), the processor  60 ( n −1), and the amplifier PA(n−1) in  FIG. 14 . The beam characteristics measurement unit  40 ( k +1) and the processor  60 ( k +1) in  FIG. 15  may correspond to the beam characteristics measurement unit  40 ( n ) and the processor  60 ( n ) in  FIG. 14 . 
     In  FIG. 15 , the beam characteristics measurement unit  40 ( k ), the wavefront controller  50 ( k ), and the amplifier PA(k) may be identical in configuration and function to those of the first embodiment. 
     As shown in  FIG. 15 , the beam splitter  41  of the beam characteristics measurement unit  40 ( k +1) may split the pulse laser beam  30  into a third beam path B 3  and a fourth beam path B 4 . The beam splitter  41  of the beam characteristics measurement unit  40 ( k +1) may correspond to the second beam splitter of the present disclosure. The transfer optical system  44  and the optical sensor  45  may be provided in the third beam path B 3 . The optical sensor  45  of the beam characteristics measurement unit  40 ( k +1) may correspond to the second optical sensor of the present disclosure. The downstream wavefront controller  50 ( k +1) (not shown) may be provided in the fourth beam path B 4 . 
     The processor  60 ( k +1) may transfer, to the processor  60 ( k ), data that is outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). The processor  60 ( k ) may control the wavefront controller  50 ( k ) on the basis of this data. 
     Data that is outputted from the beam waist measuring instrument  46  of the beam characteristics measurement unit  40 ( k +1) may be used for controlling the downstream wavefront controller  50 ( k +1) (not shown), but does not need to be used for controlling the upstream wavefront controller  50 ( k ). 
     4.2 Operation 
     4.2.1 Main Flow 
       FIG. 16  is a flowchart showing an exemplary operation of the processor  60 ( k ) shown in  FIG. 15 . The processor  60 ( k ) may control the wavefront controller  50 ( k ) through the following process. 
     Steps S 100   a  to S 300   a  of the process shown in  FIG. 16  may be the same as those of the first embodiment described with reference to  FIG. 8 . A control signal that the processor  60 ( k ) transmits in step S 300   a  may correspond to the first control signal of the present disclosure. After step S 300   a , the processor  60 ( k ) may proceed to step S 400 . 
     In step S 400 , the processor  60 ( k ) may calculate a beam radius Win(k+1) on the basis of data of a beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). The beam radius Win(k+1) may be the beam radius of a pulse laser beam incident on the downstream wavefront controller  50 ( k +1). Details of this process will be described below with reference to  FIG. 17 . 
     Next, in step S 500 , the processor  60 ( k ) may determine whether the absolute value of a difference between the beam radius Win(k+1) and a target beam radius Wint is equal to or smaller than a predetermined threshold ΔWin. If the condition is not satisfied in step S 500  (S 500 ; NO), the processor may proceed to step S 600 . 
     In step S 600 , the processor  60 ( k ) may reset the target value Pwt of the focal power of the wavefront controller  50 ( k ) on the basis of the beam radius Win (k+1). In step S 600 , the target value Pwt of the focal power may be set so that the beam radius Win(k+1) becomes closer to the target beam radius Wint. Details of this process will be described below with reference to  FIG. 18 . 
     Next, in step S 700   a , the processor  60 ( k ) may transmit a control signal to the wavefront controller  50 ( k ) so that the focal power takes on the target value Pwt. The processing in step S 700   a  may be the same as the processing in step S 300   a , except that the target value Pwt of the focal power is reset. A control signal that the processor  60 ( k ) transmits in step S 700   a  may correspond to the second control signal of the present disclosure. 
     After step S 700   a , the processor  60 ( k ) may return to the above-described step S 400  and repeat the processing from step S 400  to step S 500 . 
     If the condition is satisfied in the above-described step S 500  (S 500 ; YES), the processor may proceed to step S 800 . 
     In step S 800 , the processor  60 ( k ) may transmit, to the EUV light generation controller  5 , a signal indicating that wavefront adjustment is OK. 
     Next, in step S 900 , the processor  60 ( k ) may determine whether to discontinue the wavefront adjustment. In a case where the processor  60 ( k ) does not discontinue the wavefront adjustment (S 900 ; NO), the processor  60 ( k ) may return to the above-described step S 400  and repeat the processing from step S 400  to step S 900 . Alternatively, the processor  60 ( k ) may return to the above-described step S 100   a . In a case where the processor  60 ( k ) discontinues the wavefront adjustment (S 900 ; YES), the processor  60 ( k ) may end the process of the present flowchart. 
     4.2.2 Calculation of Win(k+1) 
       FIG. 17  is a flowchart showing details of a process in step S 400  shown in  FIG. 16 . The process shown in  FIG. 17  may be performed by the processor  60 ( k ) as a subroutine of step S 400 . In this process, the processor  60 ( k ) may calculate the beam radius Win(k+1) of the pulse laser beam incident on the wavefront controller  50 ( k +1). 
     The process shown in  FIG. 17  may be different from the process described with reference to  FIG. 10  with regard to the first embodiment in that data of a beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1) is used. Further, the process shown in  FIG. 17  may be different from the process described with reference to  FIG. 10  with regard to the first embodiment in that a magnification Ma(k+1) of the transfer optical system  44  of the beam characteristics measurement unit  40 ( k +1) is used. In other respects, the process shown in  FIG. 17  may be the same as the process described with reference to  FIG. 10 . 
     4.2.3 Setting of Target Value of Focal Power 
       FIG. 18  is a flowchart showing details of a process in step S 600  shown in  FIG. 16 . The process shown in  FIG. 18  may be performed by the processor  60 ( k ) as a subroutine of step S 600 . The processor  60 ( k ) may reset the target value Pwt of the focal power through the following process. 
     First, in step S 601 , the processor  60 ( k ) may compare the beam radius Win(k+1) with the target beam radius Wint. 
     If the beam radius Win(k+1) is smaller than the target beam radius Wint, the processor  60 ( k ) may proceed to step S 602 , in which the processor  60 ( k ) may subtract a predetermined value ΔPw from the current target value Pwt and set the resulting value as a new target value Pwt of the focal power. 
     If the beam radius Win(k+1) is equal to the target beam radius Wint, the processor  60 ( k ) may proceed to step S 603 , in which the processor  60 ( k ) may set the current target value Pwt as a new target value Pwt of the focal power without change. 
     If the beam radius Win(k+1) is greater than the target beam radius Wint, the processor  60 ( k ) may proceed to step S 604 , in which the processor  60 ( k ) may add the predetermined value ΔPw to the current target value Pwt and set the resulting value as a new target value Pwt of the focal power. 
     Upon setting the new target value Pwt of the focal power, the processor  60 ( k ) may end the process of the present flowchart and shift to step S 700   a  shown in  FIG. 16 . 
     4.3 Working Effects 
     The second embodiment controls the wavefront controller  50 ( k ) on the basis of the beam radius Win(k+1) on the downstream side of the amplifier PA(k), thus making it possible to adjust the beam diameter of a pulse laser beam in the amplification region  73  so that the pulse laser beam may be efficiently amplified. 
     Further, the second embodiment makes it possible to control the wavefront controller  50 ( k ) on the basis of data from the beam characteristics measurement unit  40 ( k ) on the upstream side of the amplifier PA(k) before controlling on the basis of the beam radius Win(k+1) on the downstream side of the amplifier PA(k). This causes the pulse laser beam to be controlled not to strike the pair of electrodes  71  and  72  of the amplifier PA(k), thus making it possible to highly accurately control the wavefront controller  50 ( k ) on the basis of the beam radius Win(k+1) on the downstream side of the amplifier PA(k). 
     5. LASER APPARATUS THAT DETERMINES WHETHER TO PERFORM BEAM CONTROL (THIRD EMBODIMENT) 
     5.1 Main Flow 
       FIG. 19  is a flowchart showing an exemplary operation of the processor  60 ( k ) in a laser apparatus  3  according to a third embodiment of the present disclosure. A configuration of the laser apparatus  3  according to the third embodiment is neither described nor illustrated, as it is the same as the configuration of the laser apparatus  3  according to the second embodiment. The processor  60 ( k ) may control the wavefront controller  50 ( k ) through the following process. 
     First, in step S 50 , the processor  60 ( k ) may analyze a beam profile on the basis of the data of the beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). The analysis of the beam profile may include determination of the number of peaks of the beam intensity distribution and measurement of the beam radius Win(k+1). Details of this process will be described below with reference to  FIG. 20A . 
     Next, in step S 90 , the processor  60 ( k ) may determine whether a result of the analysis of the beam profile was OK or not good. If the result of the analysis of the beam profile was not good (S 90 ; NO), the processor  60 ( k ) may proceed to step S 100   a.    
     The processing from step S 100   a  to step S 300   a  may be the same as that described with reference to  FIG. 16 . After step S 300   a , the processor  60 ( k ) may return to the above-described step S 50  and repeat the processing from step S 50  to step S 90 . 
     If, in step S 90 , the result of the analysis of the beam profile was OK (S 90 ; YES), the processor  60 ( k ) may proceed to step S 500 . 
     The processing from step S 500  to step S 700   a  may be the same as that described with reference to  FIG. 16 . After step S 700   a , the processor  60 ( k ) may return to the above-described step S 50  and repeat the processing from step S 50  to step S 500 . 
     If, in step S 500 , the absolute value of the difference between the beam radius Win(k+1) and the target beam radius Wint is equal to or smaller than the predetermined threshold ΔWin (S 500 ; YES), the processor may proceed to step S 800 . 
     The processing from step S 800  to step S 900  may be the same as that described with reference to  FIG. 16 . 
     In a case where, in step S 900 , the processor  60 ( k ) does not discontinue the wavefront adjustment (S 900 ; NO), the processor  60 ( k ) may return to the above-described step  350  and repeat the processing from step S 50  to step S 900 . In a case where, in step S 900 , the processor  60 ( k ) discontinues the wavefront adjustment ( 3900 ; YES), the processor  60 ( k ) may end the process of the present flowchart. 
     5.2 Analysis of Beam Profile 
       FIG. 20A  is a flowchart showing details of a process in step S 50  shown in  FIG. 19 . The process shown in  FIG. 20A  may be performed by the processor  60 ( k ) as a subroutine of step S 50 . In this process, the processor  60 ( k ) may analyze the beam profile on the basis of the data of the beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). 
     Each of  FIGS. 20B and 20C  is a diagram for discussing the process shown in  FIG. 20A .  FIG. 20B  shows an example of the beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). The position of a pixel having a maximum beam intensity in the beam intensity distribution shown in  FIG. 20B  may be indicated by coordinates (Hmax, Vmax). In  FIG. 20B , the H axis and the V axis may intersect at a right angle at the coordinates (Hmax, Vmax). The direction of the H axis may coincide with the direction of discharge by the pair of electrodes  71  and  72 .  FIG. 20C  shows a beam intensity distribution along the H axis, i.e., a beam intensity distribution at Vmax.  FIG. 20C  shows a maximum value Imax of beam intensity in the beam intensity distribution. 
     First, in step S 51 , the processor  60 ( k ) may read out the data of the beam intensity distribution outputted from the beam profile measuring instrument  43  of the beam characteristics measurement unit  40 ( k +1). 
     Next, in step S 52 , the processor  60 ( k ) may obtain the maximum value Imax of beam intensity in the beam intensity distribution and the position (Hmax, Vmax) of the pixel having the maximum value. 
     Next, in step S 53 , the processor  60 ( k ) may set the value of a threshold Ith. The value of the threshold Ith may be set to Ith=Imax/e 2  by using the above-described maximum value Imax of beam intensity. 
     Next, in step S 54 , the processor  60 ( k ) may obtain the number Pn of peaks exceeding the threshold value Ith from the beam intensity distribution at Vmax. When the beam intensity distribution is a Gaussian distribution, the number Pn of peaks is 1. However, as shown in  FIG. 7 , when a part of a pulse laser beam strikes the pair of electrodes  71  and  72  or the like, the number Pn of peaks may be a number of 2 or greater as shown in  FIG. 20C . 
     Next, in step S 55 , the processor  60 ( k ) may determine whether the number Pn of peaks is 1. If the number Pn of peaks is 1 (S 55 ; YES), the processor  60 ( k ) may proceed to step S 56 . 
     The processing in step S 56  and step S 57  may be the same as the processing in step S 412  and step S 413  shown in  FIG. 17 . After step S 57 , the processor  60 ( k ) may proceed to step S 58 . 
     In step S 58 , the processor  60 ( k ) may determine that the result of the analysis of the beam profile is OK. After step S 58 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 90  of  FIG. 19 . 
     If, in the above-described step S 55 , the number Pn of peaks is not 1 (S 55 ; NO), the processor  60 ( k ) may determine in step S 59  that the result of the analysis of the beam profile is not good. After step S 59 , the processor  60 ( k ) may end the process of the present flowchart and shift to step S 90  of  FIG. 19 . 
     The third embodiment makes it possible to omit the processing from S 100   a  to S 300   a  shown in  FIG. 19 , provided the result of the analysis of the beam profile is OK. Therefore, the third embodiment may be simpler in process than the second embodiment. 
     6. LASER APPARATUS THAT PERFORMS BEAM CONTROL ACROSS A PLURALITY OF AMPLIFIERS (FOURTH EMBODIMENT) 
       FIG. 21  is a partial sectional view illustrating a configuration of a laser apparatus  3  according to a fourth embodiment of the present disclosure. In the fourth embodiment, the beam characteristics measurement unit  40 ( k ) and the wavefront controller  50 ( k ) do not need to be provided on the upstream side of the amplifier PA(k). The beam characteristics measurement unit  40 ( 2 ) and the wavefront controller  50 ( 2 ) may be provided on the upstream side of the second amplifier PA( 2 ). 
     The processor  60 ( 2 ) may control the wavefront controller  50 ( 2 ) on the basis of data outputted from the beam characteristics measurement unit  40 ( 2 ) so that the pulse laser beam does not strike the electrodes of the amplifiers PA( 2 ) and PA(k). Further, the processor  60 ( 2 ) may control the wavefront controller  50 ( 2 ) on the basis of data outputted from the beam characteristics measurement unit  40 ( n ) provided on the downstream side of the amplifier PA(k) so that the pulse laser beam is efficiently amplified. 
     In other respects, the fourth embodiment may be the same as the above-described second and third embodiments. 
     It should be noted that although a case has been described where the wavefront controller  50 ( 2 ) is controlled on the basis of the data outputted from the beam characteristics measurement unit  40 ( n ), the fourth embodiment is not limited to this case. The wavefront controller  50 ( k ) may be controlled across a plurality of upstream amplifiers on the basis of data outputted from a given beam characteristics measurement unit  40  (k+x). Note here that x may be an integer of 2 or greater. 
     7. OTHERS 
     7.1 Examples of Amplifier 
     7.1.1 First Example 
       FIG. 22A  is an internal transparent view illustrating a configuration of a triaxial orthogonal amplifier  79  as a first example of the amplifier PA(k).  FIG. 22B  is a cross-sectional view taken along the line XXIIB-XXIIB in  FIG. 22A . The triaxial orthogonal amplifier  79  may be an amplifier in which the travel direction of the pulse laser beam  30  passing through the amplification region  73 , the direction of flow  76   a  of a laser gas flowing through the amplification region  73 , and the direction of discharge by the pair of electrodes  71  and  72  positioned with the amplification region  73  interposed therebetween are orthogonal to one another. 
     A cross flow fan  76  and a heat exchanger  77  may be provided inside the laser chamber  70 . A motor  78  coupled to the cross flow fan  76  may be provided outside the laser chamber  70 . The motor  78  may rotate a rotating shaft of the cross flow fan  76 . The cross flow fan  76  may generate the flow  76  of the laser gas inside the laser chamber  70 . The heat exchanger  77  may cause heat that is accumulated in the laser gas by discharge to be released out of the laser chamber  70 . 
     The other points may be the same as those described with reference to  FIG. 3 . 
     7.1.2 Second Example 
       FIG. 23  is a perspective view illustrating a configuration of a high-speed axial-flow amplifier  80  as a second example of the amplifier PA(k). The high-speed axial-flow amplifier  80  may include a discharge tube  81 , an entrance window  82 , an exit window  83 , a pair of electrodes  84  and  85 , a gas tube  86 , a heat exchanger  87 , and an air blower  88 . 
     The pulse laser beam  30  may enter the discharge tube  81  through the entrance window  82 , pass through the discharge tube  81 , and exit the discharge tube  81  through the exit window  83 . The laser gas may be circulated through the discharge tube  81  by the gas tube  86  and the air blower  88 . Application of a high-frequency voltage from a high-frequency power supply (not shown) to the pair of electrodes  84  and  85  provided at positions with the discharge tube  81  interposed therebetween may cause discharge to be generated in the discharge tube  81  to excite the laser gas to amplify the pulse laser beam  30  passing through the discharge tube  81 . The heat that is accumulated in the laser gas by the discharge may be dissipated by the heat exchanger  87  provided on the gas tube  86 . 
     It is desirable that the pulse laser beam have its wavefront adjusted so that the pulse laser beam does not strike an inner surface of the discharge tube  81 . As the values of the above-described Din and Dout, the diameter of the entrance window  82  and the diameter of the exit window  83  may be used, respectively. In this case, as the values of the above-described Zin and Zout, the position of the entrance window  82  and the position of the exit window  83  may be used, respectively. 
     7.2 Examples of Wavefront Controller 
     7.2.1 First Example 
     Each of  FIGS. 24A to 24C  is a conceptual diagram of a variable radius mirror  51  as a first example of the wavefront controller  50 ( k ). The variable radius mirror  51  may be supported by a mirror holder (not shown) in a beam path of the pulse laser beam  30 . 
     The variable radius mirror  51  may be a mirror of which the curvature of the reflective surface can be modified. The variable radius mirror  51  may be transformed to be a flat mirror as shown in  FIG. 24A . Here, the focal power Pw of the variable radius mirror  51  may be substantially 0. The variable radius mirror  51  may also be transformed to be a concave mirror with a focal length +F as shown in  FIG. 24B . Here, the focal power Pw of the variable radius mirror  51  may have a positive value. The variable radius mirror  51  may also be transformed to be a convex mirror with a focal length −F as shown in  FIG. 24C . Here, the focal power Pw of the variable radius mirror  51  may have a negative value. Thus, the variable radius mirror  51  may adjust the wavefront of a pulse laser beam. 
       FIG. 24D  is a partial sectional view illustrating a specific configuration of each of the variable radius mirrors  51  shown in  FIGS. 24A to 24C . The variable radius mirror  51  may include a pressure cavity  511 , a reflector  512 , a supply pipe  513 , a discharge pipe  514 , and a pressure adjuster  515 . 
     The pressure cavity  511  may be a rigid container in which a liquid such as water is stored. The reflector  512  may be an elastic plate fitted into an opening of the pressure cavity  511 . A reflective layer reflecting the pulse laser beam with high reflectance may be formed on one surface of the reflector  512 , and this surface of the reflective layer may be exposed to the exterior of the pressure cavity  511 . 
     One end of each of the supply pipe  513  and the discharge pipe  514  may be connected to the pressure cavity  511 . The other end of each of the supply pipe  513  and the discharge pipe  514  may be connected to the pressure adjuster  515 . 
     The pressure adjuster  515  may supply a liquid into the pressure cavity  511  through the supply pipe  513  to increase a pressure inside the pressure cavity  511  based on a control signal outputted from the processor  60 ( k ). The pressure adjuster  515  may discharge a liquid from the pressure cavity  511  through the discharge pipe  514  to decrease a pressure inside the pressure cavity  511  based on a control signal outputted from the processor  60 ( k ). 
     By increasing and decreasing a pressure inside the pressure cavity  511 , the curvature of the reflective layer of the reflector  512  may be controlled. Thus, the wavefront of the pulse laser beam  30  reflected by the reflective layer of the reflector  512  may be controlled. 
     7.2.2 Second Example 
       FIG. 25  shows a second example of the wavefront controller  50 ( k ). The wavefront controller  50 ( k ) may include an off-axis paraboloidal convex mirror  821 , an off-axis paraboloidal concave mirror  822 , flat mirrors  823  and  824 , and a mirror fixing plate  825 . 
     The off-axis paraboloidal convex mirror  821  may be fixed by a mirror holder (not shown) in the beam path of the pulse laser beam  30 . The off-axis paraboloidal convex mirror  821  may reflect the pulse laser beam  30  toward the off-axis paraboloidal concave mirror  822 . 
     The off-axis paraboloidal concave mirror  822  may be fixed to the mirror fixing plate  825  through a mirror holder (not shown). The off-axis paraboloidal concave mirror  822  may reflect the pulse laser beam  30  reflected by the off-axis paraboloidal convex mirror  821  toward the flat mirror  823 . 
     The flat mirror  823  may be fixed to the mirror fixing plate  825  through another mirror holder (not shown). The flat mirror  823  may reflect the pulse laser beam  30  reflected by the off-axis paraboloidal concave mirror  822  toward the flat mirror  824 . 
     The flat mirror  824  may be fixed by a mirror holder (not shown) in a beam path of the pulse laser beam  30  reflected by the flat mirror  823 . The flat mirror  824  may reflect the pulse laser beam  30  toward the amplifier PA(k). 
     The mirror fixing plate  825  may be movable along the double-head arrow Y through a driving mechanism (not shown). The wavefront of the pulse laser beam  30  may be adjusted by increasing or decreasing the distance from the mirror fixing plate  825  to the off-axis paraboloidal convex mirror  821  and the flat mirror  824 . To have a focal power of substantially 0, the wavefront controller  50 ( k ) may be adjusted so that the focusing point of the off-axis paraboloidal convex mirror  821  and the focusing point of the off-axis paraboloidal concave mirror  822  are the same as each other. 
     7.2.3 Third Example 
     Each of  FIGS. 26A to 26C  illustrates a configuration of a third example of the wavefront controller  50 ( k ). The wavefront controller  50 ( k ) may include a concave lens  831  and a convex lens  832 . 
     The concave lens  831  may be fixed by a mirror holder  833  at a position on which the pulse laser beam  30  is incident. The mirror holder  833  may be fixed to a fixing plate  836 . The concave lens  831  may transmit the pulse laser beam  30 . 
     The convex lens  832  may be held by a mirror holder  834  at a position on which the pulse laser beam  30  transmitted through the concave lens  831  is incident. The mirror holder  834  may be held by the fixing plate  836  through a linear stage  835 . The linear stage  835  may support the mirror holder  834  such that the convex lens  832  held by the mirror holder  834  can reciprocate relative to the fixing plate  836  along a beam axis of the pulse laser beam  30 . The convex lens  832  may transmit the pulse laser beam  30  toward the amplifier PA(k). 
     The concave lens  831  may have a front focusing point X 1  at a position separated from the principal point of the concave lens  831  by a focal length  71  toward the upstream side of the pulse laser beam  30 . The convex lens  832  may have a front focusing point X 2  at a position separated from the principal point of the convex lens  832  by a focal length F 2  toward the upstream side of the pulse laser beam  30 . As shown in  FIG. 26A , when the front focusing point X 1  of the concave lens  831  and the front focusing point X 2  of the convex lens  832  coincide with each other, the focal power of the wavefront controller  50 ( k ) may be substantially 0. 
     As shown in  FIG. 24B , the linear stage  835  may move the convex lens  832  to the downstream side of the pulse laser beam  30 , which may move the front focusing point X 2  of the convex lens  832  toward the more downstream side of the pulse laser beam  30  than the front focusing point X 1  of the concave lens  831 . Here, the focal power of the wavefront controller  50 ( k ) may have a positive value. 
     As shown in  FIG. 26C , the linear stage  835  may move the convex lens  832  to the upstream side of the pulse laser beam  30 , which may move the front focusing point X 2  of the convex lens  832  toward the more upstream side of the pulse laser beam  30  than the front focusing point X 1  of the concave lens  831 . Here, the focal power of the wavefront controller  50 ( k ) may have a negative value. 
     Thus, the wavefront controller may adjust the wavefront of the pulse laser beam  30 . 
     7.3 Configuration of Processor 
       FIG. 27  is a block diagram schematically illustrating an exemplary configuration of the processor  60 ( k ). 
     The processor  60 ( k ) in the above-described embodiments may be constituted by a general-purpose control device such as a computer or a programmable controller. For example, the processor  60 ( k ) may be constituted as described below. 
     (Configuration) 
     The processor  60 ( k ) may include a processing unit  1000 , and a storage memory  1005 , a user interface  1010 , a parallel input/output (I/O) controller  1020 , a serial I/O controller  1030 , and an analog-to-digital (A/D) and digital-to-analog (D/A) converter  1040  that are connected to the processing unit  1000 . The processing unit  1000  may include a central processing unit (CPU)  1001 , and a memory  1002 , a timer  1003 , and a graphics processing unit (GPU)  1004  that are connected to the CPU  1001 . 
     (Operation) 
     The processing unit  1000  may read out programs stored in the storage memory  1005 . The processing unit  1000  may execute read-out programs, read out data from the storage memory  1005  in accordance with the execution of the programs, or store data in the storage memory  1005 . 
     The parallel I/O controller  1020  may be connected to devices  1021  to  102   x  communicable through parallel I/O ports. The parallel I/O controller  1020  may control communication using digital signals through parallel I/O ports that is performed in the process where the processing unit  1000  executes programs. 
     The serial I/O controller  1030  may be connected to devices  1031  to  103   x  communicable through serial I/O ports. The serial I/O controller  1030  may control communication using digital signals through serial I/O ports that is performed in the process where the processing unit  1000  executes programs. 
     The A/D and D/A converter  1040  may be connected to devices  1041  to  104   x  communicable through analog ports. The A/D and D/A converter  1040  may control communication using analog signals through analog ports that is performed in the process where the processing unit  1000  executes programs. 
     The user interface  1010  may be configured to display progress of executing programs by the processing unit  1000  to an operator or to receive instructions by the operator to the processing unit  1000  to stop execution of the programs or to execute interruption processing. 
     The CPU  1001  of the processing unit  1000  may perform arithmetic processing of programs. In the process where the CPU  1001  executes programs, the memory  1002  may temporally store programs or temporally store data in the arithmetic process. The timer  1003  may measure time or elapsed time to output the time or the elapsed time to the CPU  1001  in accordance with the execution of the programs. When image data is input to the processing unit  1000 , the GPU  1004  may process the image data in accordance with the execution of the programs and output the results to the CPU  1001 . 
     The devices  1021  to  102   x  communicable through parallel I/O ports, which are connected to the parallel I/O controller  1020 , may be the EUV light generation controller  5 , another controller, or the like. 
     The devices  1031  to  103   x  communicable through serial I/O ports, which are connected to the serial I/O controller  1030 , may be the wavefront controller  50 ( k ), the uniaxial stage  49 , or the like. 
     The devices  1041  to  104   x  communicable through analog ports, which are connected to the A/D and D/A converter  1040 , may be various sensors such as the optical sensor  45  and the optical sensor  48 . 
     With the above-described configuration, the processor  60 ( k ) may be capable of achieving the operation illustrated in the flowchart. 
     The above-described embodiments and the modifications thereof are merely examples for implementing the present disclosure, and the present disclosure is not limited to these examples. Making various modifications according to the specifications is within the scope of the present disclosure, and other various modifications are possible within the scope of the present disclosure. The modifications illustrated for one of the embodiments can be applied to other embodiments as well (including the other embodiments described herein). 
     The terms used in the entirety of this specification and the appended claims should be interpreted as “non-limiting” terms. For example, the terms “include” and “be included” should be interpreted as “including the stated elements but not limited to the stated elements”. The term “have” should be interpreted as “having the stated elements but not limited to the stated elements”. Further, the modifier “one (a/an)” should be interpreted as “at least one” or “one or more”.