請用此 Handle URI 來引用此文件:
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8464
標題: | 基於相對論性雷射電漿飛鏡之模擬黑洞研究 Analog Black Hole Based on Relativistic Laser-Plasma Flying Mirror |
作者: | Yung-Kun Liu 劉詠鯤 |
指導教授: | 陳丕燊(Pisin Chen) |
關鍵字: | 類比黑洞,粒子網格模擬,雷射電漿交互作用,相對論性飛鏡,雷射電漿尾隨場, Analog Black Hole,Particle In Cell Simulation,Laser Plasma Interaction,Relativistic Flying Mirror,Laser-driven Wakefield, |
出版年 : | 2020 |
學位: | 碩士 |
摘要: | 自1974年霍金提出黑洞蒸發理論後,關於霍金輻射是否導致資訊遺失的爭議,持續吸引理論物理界之興趣。但由於宇宙中自然存在的黑洞放出之霍金輻射過於微弱,超出了目前所具備的觀測能力。為了更深入研究此問題,以及和理論預測互相驗證,在實驗室中產生「類比黑洞」的設計被陸續提出。其中一種模擬黑洞模型:飛鏡模型(Flying Mirror Model)描述一在閔考斯基空間具有特定移動軌跡的邊界,可以用來類比彎曲空間附近的物理。基於此飛鏡模型以及強場雷射在電漿中產生相對論性電子飛鏡的現象,Chen and Mourou於2017年提出了「桌上型類比黑洞實驗」(Analog Black Hole via Lasers, AnaBHEL)之構想。 本論文研究內容,主要集中於此雷射電漿飛鏡之性質,例如:此飛鏡之反射率、入射雷射及飛鏡交互作用後之反射頻譜以及如何透過改變背景電漿密度控制飛鏡軌跡等等問題。透過數值模擬及電漿理論模型,我們對於雷射電漿飛鏡進行深入的分析研究,能提供AnaBHEL實驗更多必要資訊。 在第一章中簡單回顧了霍金輻射及資訊遺失悖論的議題,以及類比黑洞的概念。我們主要介紹了類比黑洞的飛鏡模型,不同的飛鏡軌跡,會釋放出不同的能量通量 (Energy Flux)及頻譜。此外介紹了在研究雷射電漿交互作用使用的模擬工具、理論。模擬部分,我們介紹了粒子網格模擬(Particle In Cell Simulation)中用到的概念及重要的演算法。理論部分,回顧了在雷射電漿交互作用領域中用到的基本概念。 第二章我們討論了背景電漿密度是如何影響相對論性飛鏡之速度。飛鏡速度除了在類比黑洞實驗中扮演重要的角色外,也在雷射尾場粒子加速器中有著重要的影響。我們首先介紹了雷射在電漿中產生非線性尾隨場的理論。之後,我們利用此理論,對於飛鏡和驅動光的距離進行理論討論。再來介紹了在梯度電漿密度背景下,計算飛鏡速度之兩種方法。在以往文獻中,第一面相對論性飛鏡被認為和驅動雷射相距一個電漿波長,但我們透過理論研究發現,此距離和電漿波長實際相差一個係數。若無考慮此係數的修正,以上兩種估算飛鏡速度的方法,皆會高估速度的改變量。 第三章我們討論了相對論性飛鏡的反射率問題。相對論性飛鏡為一層密度極高的電子組成,其反射率可以透過估計此電子層密度分布以及解一入射電磁波在此電子層上的邊界條件、波動方程式來進行計算。我們首先回顧了過往對於此問題的研究,在將過往研究結果和我們執行的一維模擬比較時,我們發現在特定的情況下,以往之電子密度模型對反射率有高估的現象。因此我們根據模擬中的電子分布,提出不同的擬合模型,並獲得和模擬數據吻合的結果。此外,以往研究集中討論於一相對論飛鏡及平面波的交互作用。本章後半,我們將此理論延伸至具有有限脈寬的入射波(以高斯分布為例),發現有限脈寬入射波的反射頻譜,其峰值會和平面波結果具有一定偏移。 Since Hawking proposed the theory of black hold evaporation in 1974, the debate that whether Hawking radiation causes information loss attracts theoretical physicists. One way to set down the debate is through direct observation. However, the Hawking radiation emitted by astrophysical black holes is too weak to be observed due to the large mass of black hole. To dig into this issue and verify the theoretical predictions, several schemes of ``Analog Black Hole' had been proposed to observe the black hole radiation in the Lab. One of these Analog Black Hole models, the flying mirror model, describes that a boundary with specific trajectory in Minkowski space can mimic the physics around curved-spacetime. On the basis of this model and the phenomenon that an intense laser can generate a relativistic flying mirror in plasma, Chen and Mourou proposed the experiment ``Analog Black Hole via Lasers, AnaBHEL'. This thesis mainly focuses on properties of laser-driven flying plasma mirror, such as the reflectivity, the reflected spectrum as an incident laser pulse interacts with the mirror and the relation between the trajectory of the flying mirror and the background plasma density. These studies are based on numerical simulations and cold collision-less plasma theory. These studies can provide essential information for the AnaBHEL experiment. In chapter 1, we briefly review the issue about Hawking radiation, information loss paradox and proposals about analog black hole. In the flying mirror model, different trajectories of the flying mirror emit different energy flux and frequency spectrum. Besides, we introduce the simulation tool and the theory to study laser plasma interaction. In simulation part, we explain the concept and algorithm of Particle In Cell simulation. In theory part, we review the basic plasma theory and the interaction between laser and plasmas. In chapter 2, we describes how the background plasma density affects the velocity of the flying mirror. The velocity of mirror plays an important role in not only analog black hole experiment but also the Laser Wake Field Accelerator (LWFA). We first introduce the one-dimensional nonlinear theory of the laser-driven wakefield and utilize this theory to investigate the distance between driver laser pulse and the flying mirror. Then, we review two methods to calculate the velocity of flying mirror in an inhomogeneous plasma background. In previous literature, the distance between first plasma mirror and the driver is thought to be a plasma wavelength. However, we find the distance differs from plasma wavelength by a coefficient. With this corrected term, the velocity of flying mirror can be calculated more accurately. In chapter 3, we study the reflectivity of the flying mirror. The relativistic flying plasma mirror is composed with a dense shell of electrons. The reflectivity can be estimated by the density distribution of electrons and solving the wave equations with proper boundary condition of an incident wave. First, we review previous studies on this problem. We found previous model of the electron distribution seems to overestimate the reflectivity compared to 1D simulation results. Therefore, we proposed a density distribution fitting model and get results which agree well with simulation data. Besides, previous study mainly discussed the interaction between the flying mirror and a plane incident wave. In the second half of this chapter, we extend the study to a finite bandwidth incident wave (the Gaussian profile is considered). We find a deviation of the peak frequency of reflected spectrum exists compared to the result of a plane wave. |
URI: | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/8464 |
DOI: | 10.6342/NTU202001324 |
全文授權: | 同意授權(全球公開) |
顯示於系所單位: | 物理學系 |
文件中的檔案:
檔案 | 大小 | 格式 | |
---|---|---|---|
U0001-0507202020530100.pdf | 1.58 MB | Adobe PDF | 檢視/開啟 |
系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。