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当放电电压为10kV时,诱导激光能量为140mJ,得到放电电压电流波形,如图 2所示。虚线表示放电电压的变化,实线表示电流的变化。粗点线表示激光作用时刻,t0=100ns时,激光到达靶材表面,重新定义此时刻为放电开始t=0时刻。在约t=20ns时,电流形成一个几十安培的小峰,电压出现几百伏特的凹陷,这是由激光等离子体扩散到阳极引起的。在t=100ns后,稳定击穿开始形成,放电由电流烧蚀靶材产生的等离子体维持,电压下降,电流上升,约t=1300ns时电流达到第1个峰值900A,随后电压电流出现衰减振荡,整个放电阶段持续约14μs后电极恢复绝缘,等待下一个激光脉冲到来后电极再次击穿。选取a~i细点线对应的第1个半周期的时刻点,进行等离子体图像的时域变化分析。
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当放电电压为10kV、诱导激光能量为140mJ时,设置ICCD曝光时间5ns,延时间隔150ns,得到不同时刻的等离子体羽辉图像,如图 3所示。图 3a~图 3i分别对应着图 2中虚线a~i对应的时刻点,图 3a中虚线对应电极表面。a时刻,激光作用锡靶刚结束,电流开始上升,等离子体羽辉主要由激光等离子体形成,此时阴极等离子体刚扩散到阳极表面; b~f阶段,电流迅速上升,阴极和阳极等离子体连接在一起形成放电通道,放电等离子体羽辉开始占主,电弧近似“圆柱形”; f时刻,电流接近峰值,羽辉膨胀达到最大,电极间隙中心位置出现最大电弧直径,约为5mm; g时刻,靠近阴极的电弧半径收缩由于收缩更快,电弧呈现“圆锥形”; h时刻,近阴极处出现电弧最小直径,约为2mm,此时电弧开始呈现“抛物线形”; h~i阶段,电流开始下降,靠近阴极的电弧半径开始重新扩大。
电弧的膨胀和收缩与等离子体的热膨胀力p(p=kBNeTe,kB为玻尔兹曼常数,Ne为电子密度,Te为电子温度)与电流形成的磁场带来的径向磁压力pz(pz=μ0I2/(2πr),μ0为真空磁导率,I为电流,r为电弧半径)的比值有关[23],而等离子体的温度和密度变化和电流产生的焦耳热有关,因此电流的变化同时影响p和pz,是电弧形态变化的主要原因。靠近阴极处,由于较大电流密度影响[24],电弧收缩更剧烈。
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保持诱导激光能量和曝光时间不变,改变延时间隔为100ns,在电压U为7kV和8kV的条件下进行拍摄。为了方便电弧大小的对比,实验中对图像进行轮廓提取[25],将轮廓提取后获得的图像面积定义为电弧面积[26],不同电压下电弧面积如图 4所示。实线和虚线分别代表不同电压下电流,可以看到, 电压不影响电流的上升和下降时间,只是影响电流峰值大小。圆形与方形散点代表电弧面积,在电流刚开始上升阶段,由于热膨胀作用远远强于箍缩效应,电弧面积迅速增加,在电流接近峰值时,电弧面积扩散达到最大。在电流峰值时刻,箍缩效应强于热膨胀作用,电弧面积短暂下降。在电流下降阶段,箍缩效应减弱,等离子又进入膨胀阶段,电弧面积开始上升。随后由于电流产生的等离子体速率跟不上等离子膨胀的速度,电弧进入消散阶段,电弧面积又急剧下降。不同电压下,电弧面积的变化都满足这一趋势。高电压下单位时间靶材产生的等离子体密度更大,电弧的面积更大,产生的等离子体能量更大,电弧面积膨胀到最大所需时间更长,在电弧消散阶段,电弧面积减小的速率也要更慢一些。
改变延时间隔为50ns,可以看到, t从1000ns~1100ns时,10kV对应的电弧轮廓变化如图 5a~图 5c所示,7kV对应的电弧轮廓变化如图 5d~图 5f所示。电流峰值时刻,靠近阳极的电弧半径基本不变,靠近阴极的电弧半径持续减小。在电压7kV时,由于瑞利泰勒不稳定性的影响[27],1100ns时电弧出现了断开的现象,而电压10kV时,电弧在1100ns时仍然可以维持较小的半径,可见高电压有助于维持电弧的稳定。
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放电电压为10kV、电极间距为5mm时,改变诱导激光能量得到不同激光能量下放电等离子体图像,如图 6所示。图 6a、图 6b和图 6c分别对应t=0ns时刻激光能量为55mJ, 90mJ和140mJ的等离子体羽辉图像,此时羽辉主要由激光等离子体在电场中加速膨胀形成,高温区集中在阳极和阴极表面。初始激光能量越高,等离子羽辉面积越大。400ns时刻,等离子体羽辉主要由放电等离子体形成。诱导激光能量为55mJ时,阳极等离子体和阴极等离子体还未连接在一起,如图 6d所示。诱导激光能量为90mJ时,阳极等离子体和阴极等离子体刚开始连接,未形成稳定的电弧,如图 6e所示。诱导激光能量为140mJ时,红色高温区连接在一起,电极间已经形成稳定的电弧,如图 6f所示。诱导激光的能量影响电弧形成的时间,激光能量越大,产生的初始等离子体的密度更大、能量更高,稳定电弧越早形成,越有利于EUV的产生。
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利用1维近似的真空电弧磁流体动力学简化模型[28],可以得到电流一定时电极间隙中不同位置z和电弧截面S(z)的关系:
$ S(z)=S_{0}(z+R)^{m} / R^{m} $
(1) 式中, S0表示阴极处电弧截面面积,z表示放电轴上距离阴极的距离,R表示阴极处弧斑半径,常数m取决于电流密度的大小。在本文中的电流范围内,m取值在0~2。m=0时, 电弧呈现“圆柱形”; m=1时, 电弧呈现“圆锥形”; m=2时, 电弧呈现“抛物线形”。这3种形态对应图 3不同时刻出现的3个形态。
由下式可以得到电极间隙中等离子温度分布:
$ \left\{\begin{array}{l} x=(z+R) / R \\ T=T_{\mathrm{e}} / T_{\mathrm{e}, 0} \\ K_{0}=e I /\left(T_{\mathrm{e}, 0} \sigma_{0} \pi R\right) \\ A=5 K_{0} /(2 m+3) \\ T^{5 / 2}=(1-A) x^{-5 m / 3}+A x^{1-m} \end{array}\right. $
(2) 式中, Te, 0为阴极表面的电子温度,T为归一化电子温度,I为电流,e为电子电荷量,σ0为等离子体电导率。
当电流为600A和800A时,通过对等离子体羽辉图像轮廓进行提取,用(1)式进行拟合,m分别为1.7和1.1时拟合效果最佳。假定阴极表面附近的电子温度保持2.1eV不变,锡烧蚀率等边界条件由参考文献中获得,利用(2)式计算得到不同电流条件下电极间隙内电子温度分布, 如图 7所示。可以看到, 随着电流的增加,阳极附近的电子温度显著增加。这和实验观测到的羽辉现象吻合,也和ZHU等人[2]测得的电子温度数量级一致。
激光诱导放电等离子体羽辉的研究
Investigation of plume of laser-induced discharge plasma
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摘要: 为了研究激光诱导放电等离子体的膨胀特性,建立了一套基于脉冲CO2激光诱导锡靶放电等离子体极紫外光源装置,采用增强型电荷耦合器件对羽辉进行拍摄,并采用1维真空电弧模型对实验结果进行了理论说明。实验中改变放电电压和激光能量,得到了不同条件下时间分辨的羽辉图像。结果表明,在激光能量140mJ、放电电压10kV的条件下,获得了稳定的放电等离子体;等离子体的羽辉形态与电流存在对应关系,经历了形成、膨胀、收缩、再次膨胀和消散的不同阶段,放电电压和诱导激光能量对羽辉大小、稳定性和形成时间有影响。此研究有助于提高激光诱导放电等离子体光源的稳定性以及极紫外光的输出功率。
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关键词:
- 激光技术 /
- 激光诱导放电等离子体 /
- 锡 /
- 羽辉图像
Abstract: In order to study the expansion characteristics of laser-induced discharge plasma (LDP), a set of extreme ultraviolet source for tin target discharge plasma based on pulsed CO2 laser was established. The plume was photographed by intensified charge-coupled device. 1-D vacuum arc model was used to explain the experimental results. The time-resolved plume images under different conditions were obtained by changing the discharge voltage and laser energy. The results show that, under the condition of 140mJ laser energy and 10kV discharge voltage, a stable discharge plasma was obtained. There is a corresponding relationship between the plume morphology and the current. It has undergone different stages of formation, expansion, contraction, re-expansion and dissipation. Discharge voltage and induced laser energy have effects on plume size, stability and formation time. This study is helpful to improve the stability of LDP source and the output power of extreme ultraviolet light.-
Key words:
- laser technique /
- laser-induced discharge plasma /
- tin /
- plume image
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