外文翻譯--利用修改后的邁克耳孫干涉儀進(jìn)行長度測量的初步結(jié)果

1、<p><b>　　中文2590字</b></p><p><b>　　畢 業(yè) 設(shè) 計(jì)</b></p><p>　　外 文 文 獻(xiàn) 譯 文 及 原 文</p><p>　　學(xué) 生： </p><p>　　學(xué) 號：

2、 </p><p>　　院 （系）： 電氣與信息工程學(xué)院 </p><p>　　專 業(yè)： 電子信息工程 </p><p>　　指導(dǎo)教師： </p><p>　　2013年6月 6日</p><p>　　利用修改后的邁克耳孫干

3、涉儀進(jìn)行長度測量的初步結(jié)果</p><p>　　林栩凌 張建兵 雒峰 卑華 陸善良 俞鐵民 戴志敏</p><p>　　1（上海應(yīng)用物理研究所,中國科學(xué)院，上海 201800）</p><p>　　2（研究生院的中國科學(xué)院,北京100049,中國）</p><p>　　摘要:基于飛秒加速器的裝置，該裝置建造在上海應(yīng)用物理研究所(SINAP),

4、最近一個(gè)經(jīng)修改后的遠(yuǎn)紅外邁克耳孫干涉儀通過光學(xué)自相關(guān)方法，已經(jīng)被用來測量電子光束的長度。相比較于之前常規(guī)的邁克耳孫干涉儀,我們使用一個(gè)空心回射器而不是一個(gè)平面反射鏡的反射鏡。本文將為大家介紹實(shí)驗(yàn)設(shè)置和長度測量的結(jié)果。</p><p>　　關(guān)鍵詞：飛秒線性加速器，長度串，干涉儀，空心回射器</p><p><b>　　1 介紹</b></p><p&

5、gt;　　最近關(guān)于電子脈沖壓縮的實(shí)驗(yàn)產(chǎn)生高峰值電流和亮度飛秒電子串。關(guān)于短束源自于高質(zhì)量光束的潛在應(yīng)用要求這方面一起了廣泛興趣。高質(zhì)量的核物理加速器,自由電子激光器驅(qū)動(dòng)加速器,下一代線性對撞機(jī),第四代光源都需要短時(shí)間光束脈沖。同時(shí),在進(jìn)程中對診斷的短電子串的研究也起了重要作用。有幾種已經(jīng)使用或正在開發(fā)的方法去測量短電子串的長度。這些一般分為兩類:頻域方法和時(shí)域方法。眾所周知，在時(shí)域測量長度的方法中使用條紋相機(jī)，條紋相機(jī)已經(jīng)證實(shí)是限于串長

6、度超過200 fs，此外,條紋相機(jī)昂貴并且測量系統(tǒng)復(fù)雜。</p><p>　　相對于時(shí)域測量方法，頻域測量使用相干過渡輻射(CTR)從金屬箔在測量飛秒脈沖的短電子中已經(jīng)顯現(xiàn)出前景。</p><p>　　本文我們首先從短電子串方面給出了基于一代的高強(qiáng)度相干渡越輻射的理論和試驗(yàn)研究,然后討論該方法基于相干渡越輻射測量束飛秒的長度,并從改進(jìn)電子實(shí)驗(yàn)裝置給出了串長度測量的結(jié)果。最后,我們分析了空氣

7、濕度對串長度測量的影響，并且闡釋了對未來研究的計(jì)劃。</p><p><b>　　2 理論背景</b></p><p>　　2.1 相干渡越輻射</p><p>　　源自于相對論性電子串輻射如同步加速器輻射躍遷輻射等，本質(zhì)上有較廣的范圍，如果輻射的波長短于電子串長度，這個(gè)階段的輻射電子不同于彼此，所以輻射是不連貫的。另一方面,如果波長較長的串長

8、度，輻射是連貫的并且輻射強(qiáng)度的平方成正比每串?dāng)?shù)字電子。光譜強(qiáng)度發(fā)出一束N粒子：</p><p><b>　?。?-1）</b></p><p>　　這里是靠單電子輻射的強(qiáng)度，是串形成因素，這是傅里葉變換的規(guī)范化的電子密度分布。對于一個(gè)相對橫向尺寸小于長度的物體，形狀因子就為</p><p><b>　?。?-2）</b>&

9、lt;/p><p>　　其中n是單位向量從群到觀測點(diǎn)的中心，z是電子相對于堆中心的位置向量。顯然,測量的輻射譜將通過傅里葉變換給出形成因素和電子密度分布。</p><p>　　2.2 電子串長度測量</p><p>　　電子串長度往往是通過自相關(guān)的CTR信號與一個(gè)邁克耳孫干涉儀進(jìn)行測量，干涉儀是由一分束器，一個(gè)固定的平面反射鏡和一個(gè)可移動(dòng)的平面鏡組成。光進(jìn)入邁克耳孫干涉

10、儀是被光分束器分成兩部分，這兩部分在兩個(gè)不同的方向運(yùn)行，并被鏡子反射回來。經(jīng)過反射后的兩個(gè)輻射脈沖組合成一個(gè)戈利檢測器來測量光強(qiáng)度。</p><p>　　得到的干涉圖是通過測量探測器信號在兩個(gè)分路的差異作為路徑功能。測量能量的調(diào)配輻射脈沖來自于固定鏡子，，從可移動(dòng)的鏡子輻射延遲的時(shí)間，。這里和是反射和透射系數(shù)的分束器。強(qiáng)度測量探測器可以表示為</p><p><b>　　（2-3

11、）</b></p><p>　　其中是光速差，c是光速?；蛘?可以在頻域從動(dòng)臂通過添加一個(gè)額外的相位差和角頻率得到類似的表達(dá)式。</p><p>　　因此,總能量檢測器測定表達(dá)為：</p><p><b>　?。?-4）</b></p><p>　　方程式（3）和（4）可以通過傅里葉變換轉(zhuǎn)換成</p&g

12、t;<p><b>　?。?-5）</b></p><p>　　基線定義為δ→∞±強(qiáng)度,其中兩個(gè)脈沖完全分離，因此，我們有：</p><p><b>　?。?-6）</b></p><p>　　通過定義，干涉圖可以寫作：</p><p><b>　　（2-7）<

13、;/b></p><p>　　公式（7）中可表示為：</p><p><b>　　（2-8）</b></p><p>　　這里，用公式（1）和關(guān)系式，形成因子可以表示成：</p><p><b>　?。?-9）</b></p><p>　　因此，干涉圖包含頻率譜的相干渡

14、越輻射并可以用來推導(dǎo)出串長度，對于一些與高斯縱向分布：</p><p><b>　?。?-10）</b></p><p><b>　　干涉圖就變成：</b></p><p><b>　?。?-11）</b></p><p>　　高斯干涉圖的FWHM是，因此，高斯分布的等式長度是

15、的干涉圖FWHM。</p><p><b>　　3 實(shí)驗(yàn)說明</b></p><p>　　目前這個(gè)試驗(yàn)是在飛秒加速器太赫茲SINAP研究中心，主要由熱電子射頻槍，一個(gè)磁鐵，和斯坦福直線加速器中心(斯坦福線性加速器中心)類型加速管。的磁鐵是用于產(chǎn)生壓縮束的熱離子射頻槍，然后電子束是經(jīng)由槍到直線加速器形成，最后由SLAC類型管增加到20-30伏，具有高亮度的相干太赫茲輻射

16、將發(fā)出超短束通過鋁箔。</p><p>　　眾所周知，邁克耳孫干涉儀主要取決于最大光程差的兩部分相干光。然而，如果鏡子的衛(wèi)面在整個(gè)掃描中保持良好對齊，如果光通過干涉儀是足夠平行，那么這是唯一正確的。然而，把平面鏡移歪或擺動(dòng)，因?yàn)樗磻?yīng)緩慢，這樣就不會(huì)總是垂直入射電子束。這使光來自反射的動(dòng)鏡偏離了光軸的探測器，如圖1所示：</p><p>　　圖1 傾斜移動(dòng)鏡子使重組光束偏離邁克耳遜光學(xué)顯示

17、光軸的原理圖</p><p>　　為了計(jì)算最大允許鏡傾斜，我們首先對圓形的光斑鏡子引入了調(diào)制效率，可以寫成：</p><p><b>　?。?-1）</b></p><p>　　在這里是調(diào)制效率,是第一類貝塞爾函數(shù),給定：</p><p><b>　?。?-2）</b></p><

18、;p>　　是波數(shù)率(cm-1)， 是傾斜角度(弧度)，是光斑的半徑(厘米)。</p><p>　　作為一般規(guī)則,一個(gè)令人滿意的調(diào)制效率必須滿足：</p><p><b>　?。?-3）</b></p><p><b>　　（3-4）</b></p><p>　　根據(jù)科恩公式，公式（12）可約等

19、于：</p><p><b>　　（3-5）</b></p><p>　　這里。假設(shè)= 100cm?1，r = 2.5cm，要求容許鏡傾斜保持在,或弧秒。根據(jù)上面的分析, 在整個(gè)掃描過程中必須使小于58.7弧秒。</p><p>　　圖2 回射的空心反光鏡特性</p><p>　　要克服邁克耳孫干涉儀傾斜的影響,我們的解

20、決方案是用空心反光鏡取代平面鏡。一個(gè)空心反光鏡是一個(gè)由三個(gè)相互正交的鏡子組成的裝置。對于我們的實(shí)驗(yàn)，空心回射器是由埃德蒙公司制造(NT46-189)；因?yàn)辄S金具有良好的反射率，在太赫茲的地區(qū)范圍內(nèi)，所有的三鏡都是金屬涂層。</p><p>　　最重要的優(yōu)點(diǎn)是利用空心反光鏡可以將返回光沿著一條平行入射光的路徑。因此，需要精度為小于平面鏡的1或2數(shù)量級，干涉儀的精度是由空心回射器本身(NT46-189)的最大寬偏差是

21、5弧秒)和空心反光鏡位置的移動(dòng)決定的，空心反光鏡的回射特性見圖2。</p><p><b>　　4 測量結(jié)果和分析</b></p><p>　　得到的長度測量干涉圖顯示在圖3，由于分束器效率的影響，測量的干涉圖的FWHM似乎小于實(shí)際值。因此校正就很有必要，我們通過調(diào)查獲得的分束器的功率譜影響。對于高斯束的FWHM之間的關(guān)系，糾正后和實(shí)測的FWHM顯示在圖4。FWHM的

22、測量值224µm表示高斯束長度為74µm或248 fs。</p><p>　　圖3 長度測量干涉圖</p><p>　　圖4 修正和測量FWHM高斯束之間的關(guān)系</p><p><b>　　5 后續(xù)工作</b></p><p>　　我們開發(fā)并描述了系統(tǒng)產(chǎn)生的飛秒長度串，通過初步改善的邁克耳孫干涉儀進(jìn)行

23、了邁克耳孫干涉法對飛秒CTR電子串的測量，在半最大值在CTR干涉法下取得了長度值約248 fs。然而，在大氣環(huán)境中太赫茲光被強(qiáng)烈吸收，這將影響測量的準(zhǔn)確度。根據(jù)Birch原理，雖然水吸收不會(huì)影響整體的形狀譜，但將擴(kuò)大串長度，這可以解釋為由于水蒸氣在潮濕的空氣擴(kuò)大分散。因?yàn)槌睗竦目諝庹凵渎什皇枪潭ㄔ谔掌澐秶鷥?nèi)，不同的頻率有不同傳播速度。因此，當(dāng)它穿過空氣時(shí)輻射脈沖傳播，我們計(jì)算了在潮濕的空氣下的真空干涉圖，兩種情況下的干涉圖如圖5所示，

24、其中顯示了增加在空氣中的干涉圖寬度測量，所以為了更好的精度，有必要把干涉儀放在真空中測量。</p><p>　　圖5 在真空(固體)和在潮濕的空氣(虛線)的干涉圖對比</p><p>　　(E = 20MeV,Q = 0.05nC,z = 200 fs)</p><p>　　Preliminary result of bunch length measurement

25、</p><p>　　using a modified Michelson interferometer</p><p>　　LIN Xu-Ling，ZHANG Jian-Bing,，LUO Feng，BEI Hua</p><p>　　LU Shan-Liang，YU Tie-Min，DAI Zhi-Min</p><p>　　1 (Sha

26、nghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800, China) 2 (Graduate University of Chinese Academy of Sciences, Beijing 100049, China) </p><p>　　Abstract：Based on the femtosec

27、ond accelerator device which was built at the Shanghai Institute of Applied Physics (SINAP), recently a modified far infrared Michelson interferometer has been developed to measure the length of electron bunches via the

28、optical autocorrelation method. Compared with our former normal Michelson interferometer, we use a hollow retroreflector instead of a flat mirror as the reflective mirror. The experimental setup and results of the bunch

29、length measurement will be des</p><p>　　KEY WORDS：femtosecond linear accelerator, bunch length, interferometer, hollow retroreflector </p><p>　　1 Introduction </p><p>　　Recent exper

30、iments on electron pulse compression have produced femtosecond electron bunches with a high peak current and brightness. Interest in short bunches arises from the requirements of high beam quality in potential applicatio

31、ns. High quality nu- clear physics accelerators, free electron laser drive ac- celerators, next generation linear colliders, and fourth generation light sources all require short time dura- tion beam pulses [1] . Simulta

32、neously, research into the diagnostics of the sh</p><p>　　Instead of time-domain methods, frequency-domain measurements using coherent transition radiation (CTR) from metallic foils have shown promise in the

33、 measurement of very short femtosecond electron pulses. </p><p>　　In this paper we first present a theoretical and experimental investigation on the generation of high intensity coherent transition radiation

34、 from short electron bunches, then discuss the method based on coherent transition radiation to measure the bunch length of femtosecond electron bunches, and then the improved experimental setup and results of the bunch

35、length measurement are given. Finally, we analyze the e?ects of humidity in air on bunch length mea- surements and explain the plan for fut</p><p>　　2 Theoretical background </p><p>　　2.1 Cohere

36、nt transition radiation</p><p>　　Radiation from a relativistic electron bunch such as synchrotron radiation, transition radiation, etc. intrinsically has a broad spectrum. If the wavelength of the radiation

37、is shorter than the electron bunch length, the phases of the radiation emitted by the electrons di?er from each another, so the radiation is incoherent. On the other hand, if the wavelength is longer than the bunch lengt

38、h, the radiation is coherent and the intensity of the radiation is proportional to the square of the elect</p><p><b>　　(2-1)</b></p><p>　　where is the intensity radiated by a single

39、 electron and f(λ) is the bunch form factor [3, 4] , which is the Fourier transform of the normalized electron density distribution S(z). For a relativistic bunch whose transverse dimension is small compared to the lengt

40、h, the form factor becomes </p><p><b>　　(2-2)</b></p><p>　　where n is the unit vector pointing from the center of the bunch to the observation point and z is the position vector of t

41、he electron relative to the bunch center. Obviously, a measurement of the radiation spectrum will give the form factor and the electron density distribution through the Fourier transform. </p><p>　　2.2 Elect

42、ron bunch length measurement </p><p>　　Measurement of electron bunch length is often done by examination of the autocorrelation of the CTR signal with a Michelson interferometer [5] . The interferometer is c

43、omposed of a beam splitter, a fixed flat mirror and a movable flat mirror. The light en- tering the Michelson interferometer is split into two parts by the beam splitter. The two parts travel in two di?erent directions a

44、nd are reflected back by the mirrors. After reflection the two radiation pulses are combined again and transmitt</p><p>　　The interferogram is obtained by measuring the detector signal as a function of the p

45、ath di?erence in the two arms. The measured energy of the recombined radiation pulses are the radiation pulses from the fixed mirror, , and the radiation from the movable mirror delayed in the time , . Here and are the

46、 reflection and transmission coe?cients of the beam splitter. The intensity measured at the detector can be expressed as</p><p><b>　　(2-3)</b></p><p>　　where is the optical path di?

47、erence, c is the speed of light. Alternatively, a similar expression can be obtained in the frequency domain by adding an extra phase di?erence to the radiation from the movable arm at angular frequency . Thus, the tota

48、l energy measured at the detector is expressed as</p><p><b>　　(2-4)</b></p><p>　　and Eqs. (3) and (4) are related by the Fourier transform</p><p><b>　　(2-5)</b&

49、gt;</p><p>　　The baseline is defined as the intensity at δ → ±∞, where the two pulses are totally separated, hence, we have </p><p><b>　　(2-6)</b></p><p>　　By defin

50、ition, the interferogram can be written as</p><p><b>　　(2-7)</b></p><p>　　Solving for in Eq.(7) yields </p><p><b>　　(2-8)</b></p><p>　　where .

51、 Using Eq. (1) and the relation the bunch form factor can be obtained from</p><p><b>　　(2-9)</b></p><p>　　hence, the interferogram contains the frequency spectrum of coherent transi

52、tion radiation and can be used to derive the bunch length. </p><p>　　For a bunch with Gaussian longitudinal distribution, </p><p><b>　　(2-10)</b></p><p>　　the interferog

53、ram becomes</p><p><b>　　(2-11)</b></p><p>　　and the FWHM of this Gaussian interferogram is . Therefore, the equivalent bunch length for a Gaussian bunch distribution is times the i

54、nterferogram FWHM. </p><p>　　3 Description of the equipment </p><p>　　The present experiment was performed at the Femtosecond Accelerator in the THz Research Center of SINAP, which mainly consis

55、ts of a thermionic RF gun, an magnet, and a SLAC (Stanford Linear Accelerator Center) type accelerating tube. The magnet is used to compress the bunches produced by the thermionic RF gun. Then the electron beam is tran

56、sported through the gun-to-linac beam line and finally accelerated up to 20—30 MeV by a SLAC type tube. Coherent THz radiation with high brightness will be </p><p>　　It is well known that the resolution of a

57、 Michelson interferometer is mainly determined by the maximum optical path di?erence of the two parts of coherent light. However, this is only true if the planes of the mirrors remain in good alignment throughout the ent

58、ire scan and if the light that passes through the interferometer is su?ciently collimated. However, the moving flat mirror tends to tilt or wobble as it is retarded and, as such, will not always be perpendicular to the i

59、ncident beam. This </p><p>　　Fig. 1. Schematic diagram of the Michelson optics showing how tilting the moving mirror causes the recombinant beams to diverge from the optical axis.</p><p>　　In or

60、der to calculate the maximum allowable mirror tilt, we introduce first the modulation e?ciency in the case of the circular shape of the light spot on the mirrors, which could be written as </p><p><b>　

61、　(3-1)</b></p><p>　　where is the modulation e?ciency, is the first order Bessel function, with a given by </p><p><b>　　(3-2)</b></p><p>　　is the wave number of i

62、nterest (cm ?1 ), is the tilt angle (radians) and is the radius of the light spot (cm). </p><p>　　As a general rule, a satisfactory modulation e?ciency must satisfy [7]</p><p><b>　　(3-3)

63、</b></p><p><b>　　(3-4)</b></p><p>　　According to Cohen [8] , Eq. (12) can be approximated by </p><p><b>　　(3-5)</b></p><p>　　where . Assu

64、ming = 100cm?1，r = 2.5cm requires that the allowable mirror tilt be kept at a value of , or arc seconds. According to the above analysis, must therefore be less than 58.7 arc seconds throughout the entire scan. </p&

65、gt;<p>　　Fig. 2. The retroreflection property of the hollow retroreflector.</p><p>　　To overcome the e?ect of tilt in our former Michelson interferometer, our solution is to replace the flat mirror by

66、 a hollow retroreflector. A hollow retroreflector is a device made up of three mutually orthogonal reflective mirrors. For our experiment the hollow retroreflector was made by the Edmund corporation (NT46-189); because g

67、old has a good reflectivity in the THz region, all the three mirror are metal coated. The most important advantage of the hollow retroreflector is the fact that it c</p><p>　　4 Measurement result and analysi

68、s</p><p>　　The interferogram obtained from a bunch length measurement is shown in Fig.3. Because of the impacts of the beam splitter e?ciency, the measured FWHM of the interferogram appears to be narrower th

69、an the real value [9]. Therefore a correction became necessary, which we obtained by investigating the beam splitter e?ects on the power spectrum. For a Gaussian bunch the relationship between the corrected F W HM and th

70、e measured FWHM is shown in Fig. 4. The measurement of 224 µm FWHM indicates a Gauss</p><p>　　Fig. 3. Interferogram from a bunch length measurement.</p><p>　　Fig. 4. The relationship betwee

71、n corrected FWHM and measured FWHM </p><p>　　for a Gaussian bunch.</p><p>　　after applying corrections due to beam splitter interferences. </p><p>　　5 Future work </p><p&

72、gt;　　A system to produce and characterize femtosecond length bunches has been developed and described. We carried out CTR Michelson interferometry for femtosecond electron bunch diagnostics by a preliminary improved Mich

73、elson interferometer. We achieved a bunch length evaluation of about 248 fs at FWHM in the CTR interferometry. However, THz light is strongly absorbed in an atmospheric environment, which will a?ect the accuracy of the m

74、easurement. According to Birch [10] , although water absorption w</p><p>　　Fig. 5. Comparison of the interferograms taken in a vacuum (solid) and in humid air (dashedline) (E = 20MeV,Q = 0.05nC,z = 200 fs)&l