Quantitative single shot and spatially resolved plasma wakefield - PowerPoint PPT Presentation

Quantitative single shot and spatially resolved plasma wakefield diagnostics Muhammad Firmansyah Kasim University of Oxford, UK PhD Supervisors: Professor Peter Norreys & Professor Philip Burrows University of Oxford, UK JAI-Fest, Oxford, 10 December 2015

Acknowledgement University of Oxford: Rutherford Appleton Laboratory: • • Peter Norreys Robert Bingham • • Philip Burrows Raoul Trines • • James Holloway Rajeev Pattathil • • Matthew Levy Dan Symes • • Naren Ratan Pete Brummitt • • Luke Ceurvorst Chris Gregory • • James Sadler Steve Hawkes AWAKE Collaboration, including: OSIRIS Consortium, including: • • Allen Caldwell Luis O. Silva • • Matthew Wing Jorge Vieira • Patric Muggli • Edda Gschwendtner Indonesian Endowment Fund for Education JAI-Fest, 10 November 2015 2 University of Oxford, RAL, UCL

Introduction JAI-Fest, 10 November 2015 3 University of Oxford, RAL, UCL

Introduction JAI-Fest, 10 November 2015 4 University of Oxford, RAL, UCL

Introduction JAI-Fest, 10 November 2015 5 University of Oxford, RAL, UCL

Introduction 𝑕 𝑧, 𝑨 = 𝑔 𝐬, 𝑨 𝑒𝐬 𝑄 JAI-Fest, 10 November 2015 6 University of Oxford, RAL, UCL

Introduction 𝑕 𝑧, 𝑨 = 𝑔 𝐬, 𝑨 𝑒𝐬 𝑄 JAI-Fest, 10 November 2015 7 University of Oxford, RAL, UCL

Introduction JAI-Fest, 10 November 2015 8 University of Oxford, RAL, UCL

Introduction Abel transform JAI-Fest, 10 November 2015 9 University of Oxford, RAL, UCL

Introduction Abel transform: ∞ 𝑠 𝑒𝑠 𝑕 𝑧, 𝑨 = 2 𝑔(𝑠, 𝑨) 𝑠 2 − 𝑧 2 𝑧 Abel transform JAI-Fest, 10 November 2015 10 University of Oxford, RAL, UCL

Introduction Abel transform: ∞ 𝑠 𝑒𝑠 𝑕 𝑧, 𝑨 = 2 𝑔(𝑠, 𝑨) 𝑠 2 − 𝑧 2 𝑧 Abel inversion: ∞ 𝜖𝑕(𝑧, 𝑨) 𝑔 𝑠, 𝑨 = − 1 𝑒𝑧 𝜌 𝜖𝑧 𝑧 2 − 𝑠 2 𝑠 Abel transform JAI-Fest, 10 November 2015 11 University of Oxford, RAL, UCL

Moving case JAI-Fest, 10 November 2015 12 University of Oxford, RAL, UCL

Moving case JAI-Fest, 10 November 2015 13 University of Oxford, RAL, UCL

Moving case 𝐝𝐩𝐭 𝜾 = 𝒘/𝒗 JAI-Fest, 10 November 2015 14 University of Oxford, RAL, UCL

Moving case 𝐝𝐩𝐭 𝜾 = 𝒘/𝒗 JAI-Fest, 10 November 2015 15 University of Oxford, RAL, UCL

Moving case Abel transform still works! 𝐝𝐩𝐭 𝜾 = 𝒘/𝒗 JAI-Fest, 10 November 2015 16 University of Oxford, RAL, UCL

Moving case Abel transform still works! How if 𝒘 > 𝒗 ? 𝐝𝐩𝐭 𝜾 = 𝒘/𝒗 JAI-Fest, 10 November 2015 17 University of Oxford, RAL, UCL

Moving case The probe goes through different longitudinal position, 𝑨 , during the interaction JAI-Fest, 10 November 2015 18 University of Oxford, RAL, UCL

Moving case The probe goes through different longitudinal position, 𝑨 , during the interaction Normal Abel transform does not work. JAI-Fest, 10 November 2015 19 University of Oxford, RAL, UCL

Forward transform • Normal Abel transformation ∞ 𝒈 𝒔, 𝒜 𝒔 𝒉 𝒛, 𝒜 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 JAI-Fest, 10 November 2015 20 University of Oxford, RAL, UCL

Forward transform • Normal Abel transformation ∞ 𝒈 𝒔, 𝒜 𝒔 𝒉 𝒛, 𝒜 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Modified Abel transformation ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 JAI-Fest, 10 November 2015 21 University of Oxford, RAL, UCL

Forward transform • Normal Abel transformation ∞ 𝒈 𝒔, 𝒜 𝒔 𝒉 𝒛, 𝒜 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Modified Abel transformation ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 where 𝒃 = 𝐝𝐩𝐭 𝜾 − 𝒘/𝒗 /𝐭𝐣𝐨 𝜾 , JAI-Fest, 10 November 2015 22 University of Oxford, RAL, UCL

Forward transform • Normal Abel transformation ∞ 𝒈 𝒔, 𝒜 𝒔 𝒉 𝒛, 𝒜 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Modified Abel transformation ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 where 𝒃 = 𝐝𝐩𝐭 𝜾 − 𝒘/𝒗 /𝐭𝐣𝐨 𝜾 , 𝒉(𝒛, 𝒍) and 𝒈(𝒔, 𝒍) are Fourier Transform of 𝒉 𝒛, 𝒜 and 𝒈(𝒔, 𝒜) in longitudinal direction, respectively JAI-Fest, 10 November 2015 23 University of Oxford, RAL, UCL

Inverse transform • Normal Abel inversion ∞ 𝝐𝒉 𝒛, 𝒜 𝒈 𝒔, 𝒜 = − 𝟐 𝒆𝒛 𝝆 𝒛 𝟑 − 𝒔 𝟑 𝝐𝒛 𝒔 JAI-Fest, 10 November 2015 24 University of Oxford, RAL, UCL

Inverse transform • Normal Abel inversion ∞ 𝝐𝒉 𝒛, 𝒜 𝒈 𝒔, 𝒜 = − 𝟐 𝒆𝒛 𝝆 𝒛 𝟑 − 𝒔 𝟑 𝝐𝒛 𝒔 • Modified Abel inversion ∞ 𝐝𝐩𝐭𝐢 𝒍𝒃 𝒛 𝟑 − 𝒔 𝟑 𝝐 𝒈 𝒔, 𝒍 = − 𝟐 𝒉 𝒛, 𝒍 𝒆𝒛 𝝆 𝒛 𝟑 − 𝒔 𝟑 𝝐𝒛 𝒔 JAI-Fest, 10 November 2015 25 University of Oxford, RAL, UCL

Application on plasma accelerators • Objective: diagnose electron density profile, 𝒐(𝒔, 𝜼) , in the wakefield • Can be done by sending the laser probe with oblique angle of incidence relative to the wakefield JAI-Fest, 10 November 2015 26 University of Oxford, RAL, UCL

Application on plasma accelerators • Objective: diagnose electron density profile, 𝒐(𝒔, 𝜼) , in the wakefield • Can be done by sending the laser probe with oblique angle of incidence relative to the wakefield • What can we detect? JAI-Fest, 10 November 2015 27 University of Oxford, RAL, UCL

Theory of photon acceleration • By photon ray theory in plasma wake (Wilks, 1989) 𝟑 ≈ − 𝝏 𝒒 𝚬𝝏 𝒅 𝝐𝒐 𝝐𝜼 𝐞𝒖 𝟑 𝝏 𝟏 𝒐 𝟏 𝟑𝝏 𝟏 JAI-Fest, 10 November 2015 28 University of Oxford, RAL, UCL

Theory of photon acceleration • By photon ray theory in plasma wake (Wilks, 1989) 𝟑 ≈ − 𝝏 𝒒 𝚬𝝏 𝒅 𝝐𝒐 𝝐𝜼 𝐞𝒖 𝟑 𝝏 𝟏 𝒐 𝟏 𝟑𝝏 𝟏 • 𝚬𝝏 and 𝝏 𝟏 : change in frequency and the central frequency of the EM wave JAI-Fest, 10 November 2015 29 University of Oxford, RAL, UCL

Theory of photon acceleration • By photon ray theory in plasma wake (Wilks, 1989) 𝟑 ≈ − 𝝏 𝒒 𝚬𝝏 𝒅 𝝐𝒐 𝝐𝜼 𝐞𝒖 𝟑 𝝏 𝟏 𝒐 𝟏 𝟑𝝏 𝟏 • 𝚬𝝏 and 𝝏 𝟏 : change in frequency and the central frequency of the EM wave • 𝒐 𝟏 and 𝒐 : the unperturbed and perturbed electron density JAI-Fest, 10 November 2015 30 University of Oxford, RAL, UCL

Theory of photon acceleration • By photon ray theory in plasma wake (Wilks, 1989) 𝟑 ≈ − 𝝏 𝒒 𝚬𝝏 𝒅 𝝐𝒐 𝝐𝜼 𝐞𝒖 𝟑 𝝏 𝟏 𝒐 𝟏 𝟑𝝏 𝟏 • 𝚬𝝏 and 𝝏 𝟏 : change in frequency and the central frequency of the EM wave • 𝒐 𝟏 and 𝒐 : the unperturbed and perturbed electron density 𝜼 : the distance in the wakefield’s frame • JAI-Fest, 10 November 2015 31 University of Oxford, RAL, UCL

Theory of photon acceleration • From photon ray theory, we get ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 JAI-Fest, 10 November 2015 32 University of Oxford, RAL, UCL

Theory of photon acceleration • From photon ray theory, we get ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Where 𝒉 𝒛, 𝜼 = 𝚬𝝏 𝒛, 𝜼 𝝏 𝟏 𝟑 𝝏 𝒒 𝒈 𝒔, 𝜼 = − 𝟐 𝝐𝒐 𝒔, 𝜼 𝒘 𝟑 𝒐 𝟏 𝝐𝜼 𝒗 𝐭𝐣𝐨𝜾 𝟑𝝏 𝟏 JAI-Fest, 10 November 2015 33 University of Oxford, RAL, UCL

Theory of photon acceleration • From photon ray theory, we get ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Where 𝒉 𝒛, 𝜼 = 𝚬𝝏 𝒛, 𝜼 𝝏 𝟏 𝟑 𝝏 𝒒 𝒈 𝒔, 𝜼 = − 𝟐 𝝐𝒐 𝒔, 𝜼 𝒘 𝟑 𝒐 𝟏 𝝐𝜼 𝒗 𝐭𝐣𝐨𝜾 𝟑𝝏 𝟏 • 𝚬𝝏 𝒛, 𝜼 can be detected using SPIDER, S 3 I, FDH, or other interferometry method. JAI-Fest, 10 November 2015 34 University of Oxford, RAL, UCL

Theory of photon acceleration • From photon ray theory, we get ∞ 𝒈 𝒔, 𝒍 𝒔 𝐝𝐩𝐭 𝒍𝒃 𝒔 𝟑 − 𝒛 𝟑 𝒉 𝒛, 𝒍 = 𝟑 𝒔 𝟑 − 𝒛 𝟑 𝒆𝒔 𝒛 • Where 𝒉 𝒛, 𝜼 = 𝚬𝝏 𝒛, 𝜼 𝝏 𝟏 𝟑 𝝏 𝒒 𝒈 𝒔, 𝜼 = − 𝟐 𝝐𝒐 𝒔, 𝜼 𝒘 𝟑 𝒐 𝟏 𝝐𝜼 𝒗 𝐭𝐣𝐨𝜾 𝟑𝝏 𝟏 • 𝒐 𝒔, 𝜼 can be obtained by the modified Abel inversion. JAI-Fest, 10 November 2015 35 University of Oxford, RAL, UCL