Preamble

Development High-Temporal-Resolution X-ray Diode Qiu-Yan Chen, Jin-Yuan Li-Juan Xiang* Laboratory Optoelectronic Devices Systems Education Guangdong Province, Shenzhen Laboratory Photonics Biophotonics, College Physics Optoelectronic Engineering, Shenzhen University, Shenzhen, China bstract X-ray diode (XRD) diagnostic system based electron pulse time-dilation energy compensation present temporal magnifier dilating temporal width electron pulse significantly improve temporal resolution. energy compensation performed using collimator ensure measurement accuracy. time-resolved anode electron detector applied detect processed electron pulse.

Theoretical studies indicate time-dilation technology increase temporal resolution Experimental verification carried using Michelson interferometer method, temporal resolution measured.

Keywords

Inertial confinement fusion X-ray diagnosis, Radiation measurement, X-ray diode

1 Introduction

Laser-driven inertial confinement fusion (ICF)

methods

transform deuterium-tritium clean nuclear energy lasts about requires measurement transient information plasma generated laser shooting. ultrafast diagnostic technology measure temperature density plasma, whose measurement basis analyzing transient fusion processes.

Typical ultrafast

diagnostic devices include X-ray streak camera, framing camera, scintillator, X-ray diode (XRD) Streak camera behave temporal resolution level. hardened streak camera Lawrence Livermore National Laboratory (LLNL) temporal resolution approximately which measured time-resolved bremsstrahlung spectrum neutron yield temporal resolution X-ray framing camera based electron pulse time-dilation technology achieve environments neutron yield Single-line-of-Sight (SLOS) framing camera based hCMOS widely

experiment

neutron yield installed COMET temporal resolution practical scintillators about materials achieve Scintillator often combined streak camera other device neutron detector paper focuses which samples radiation acquire waveform input signals functions oscilloscope neutron yield larger

experiment

X-ray radiation exists throughout entire physical process, including radiation hohlraum physics self-emission compressed plasma implosion physics. radiation measurement indispensable studying intensity temperature hohlraum radiation source, symmetry implosion, thermal nuclear burning process important ultrafast detector measure radiation detection component radiation diagnostic devices, X-ray spectrometers, flat-response composes planar anode photocathode evaporated planar metal surface, connecting coaxial cable conical connector match impedance. present,

response approximately achieved traditional However, certain physical processes fusion burning stage lasts approximately Then, higher temporal resolution desired burning plasma measurement. 2016, Hares integrated electron pulse time-dilation technology employing ramped cathode pulse paired extended drift region. configuration established transit dependency photoelectron emission timing, enabling development time-dilation (TD-XRD) prototype time-dilation mechanism involves application time-dependent photocathode-mesh structure, which generates time-varying photoelectron accelerating potential, inducing axial velocity dispersion emitted photoelectrons. photoelectron pulse traverses drift region, undergoes temporal dilation before reaching anode electron detector.

Subsequently, anode electron detector ultrafast temporal response measures temporally stretched electron pulse, thereby significantly enhancing temporal resolution TD-XRD. 2018, Gales advanced TD-XRD system, demonstrating electron pulse time-dilation technology enhanced temporal resolution 2020, further improved temporal resolution TD-XRD subsequently applied experiments which measur fusion width successfully Electron pulse time-dilation produce temporal dilation increase energy leading electrons decrease energy trailing electrons While electron pulse gradually decreasing energy bombards microchannel plate (MCP), decrease time, ecause relates energy electrons bombarding While there X-ray pulses intensity different emission times diagnosed, cause amplitude anode output pulse gradually

decrease time, resulting measurement errors. improve measurement accuracy system, enhancing uniformity essential.

Hares applied impulse voltage output surface, resulting increas voltage between faces gradually increased, thereby compensating decrease caused reduction electron energy However, compensation

method

cause energy electrons gradually decrease reach anode, pulse voltage causes acceleration voltage between output surface anode decrease time.

Electrons decreasing energy induce current pulses decreasing amplitude anode, resulting measurement errors incident X-ray amplitude information. increase uniformity without introducing measurement errors, paper proposes collimation technique compensate electron energy, ensuring energy electrons incident almost constant. collimator consists input electrode output electrode. input electrode placed drift region microstrip transmission structure, whereas output electrode input surface. input electrode center hollowed covering applying collimation pulse input electrode, output electrode grounded, time-varying accelerating electric field created between electrodes. electrons lower energy flying behind receive additional greater energy collimator electrons higher energy front, resulting electrons having nearly energy after passing through collimator. paper presents drift diagnostic system utilizes electron pulse time-dilation energy compensation.

Theoretical

analysis

performed drift

temporal resolution assessed. drift system described paper differs TD-XRD developed Hares terms enhancing uniformity terms design anode electron detector.

Hares employed conventional conical structure using conical piece connect anode effective diameter coaxial cable preserve impedance matching. paper proposes coplanar waveguide-type anode structure broadband response, which impedance tapered achieve impedance matching between anode coaxial cable. optimized design significantly improves temporal response characteristics anode. coplanar waveguide structure typically utilized high-frequency signal transmission, which recognized dispersion, bandwidth, which characteristic impedance adjusted.

Furthermore, paper implements three independent anode structures, allowing drift diagnostic system operate three separate XRDs. setup extends system's recording length, improves duration radiation measurements, enables simultaneous measurement information three distinct energy points, among other capabilities.

Moreover, input signal reconstruction algorithm proposed overcome nonlinear dilation inconsistent gain, further improve measurement accuracy system. algorithm detected anode electrical pulse signal, electron pulse temporal dilation factor D(t), reconstruct input optical signal. summary, there several differences innovations between article previous papers published Hares first article proposes electron pulse collimation technology, which compensates energy electrons time-dilation.

Then, compensation

method

achieves electron energy consistency improve

uniformity enhances system measurement accuracy ultimately. second innovative design anode structure, proposing wideband responsive coplanar waveguide anode achieve ultrafast response improve resolution. using three independent anodes, drift diagnostic system equipped three functions, which improves duration radiation measurements, third further improve measurement accuracy system, input signal reconstruction algorithm proposed.

2 Drift

diagnostic system

Schematic diagram diagnostic system electron pulse time-dilation energy compensation; Schematic diagram cathode pulse propagation Schematic diagram microstrip anode tapered transmission schematic diagram drift diagnostic system, which based electron pulse time-dilation energy compensation, shown drift diagnostic system comprises electron pulse temporal magnifier (including microstrip electron drift region), collimator (consisting input electrode input surface, which serves output electrode), anode electron detector (including anode, external circuits), high-voltage pulse generator (producing cathode collimation pulses), magnetic lens, high-speed oscilloscope. electron pulse time-dilation collimation system comprise electron pulse temporal magnifier, collimator, high-voltage pulse generator. function dilate width electron pulse, achieve temporal dilation electron pulse, compensate energy subsequent electrons, ensuring electrons incident their energy nearly uniform. electron pulse temporal magnifier comprises three microstrip anode mesh, electron drift region. transmissive microstrip structure formed evaporating thickness polystyrene film. three microstrip measure length width spaced apart other.

Microstrip serve functions. Primarily, convert incident light photoelectrons Secondly, function microstrip transmission lines, transmitting cathode pulses, thereby creating time-varying electric field between microstrip away, which

results

temporal dilation electron pulse. grounded metal nickel spatial frequency lp/mm used. applying negative voltage microstrip superimposing positive high-voltage cathode pulse,

time-varying electric field generated between plasma X-ray pulse radiation synchronized rising cathode pulse generates photoelectrons microstrip Photo lectrons produced different times acquire varying energies, leading electron velocity dispersion schematic diagram illustrating transmission cathode pulses depicted cathode pulse travels right voltage photoelectron emission point changes time. illustrated point addition voltage cathode pulse voltage superimposed point voltage Since greater total voltage between point decreases time, accelerating electric field gradually diminishes.

Consequently, earlier emitted photoelectrons obtain higher energy drift faster velocity.

After drifting through electron drift region input electrode collimator, temporal width electron pulse magnified, achieving temporal dilation electron pulse.

According above analysis, energy electron decreases while electron pulse reaches While electron pulse progressively diminishing energy directly strikes gradually diminishes time, which sequential reduction amplitude anode output signal.

However, plasma X-ray pulse radiation signals identical intensity microstrip should remain consistent, amplitude anode output signal should uniform.

Hence, reduction progressive decrease electron energy

result

measurement inaccuracies. enhance uniformity improve measurement precision drift diagnostic system, electron pulse collimation technology

presented offset electron energy loss. collimator comprises input output electrodes spaced apart, input electrode being polytetrafluoroethylene high-frequency circuit board input surface serving output electrode.

Three copper microstrip transmission lines fabricated input electrode polytetrafluoroethylene substrate, which length, width, spaced apart. small diameter created center microstrip transmission line, which covered plane density lines millimeter. connected surrounding microstrip transmission lines, allowing input electrode transmit collimation pulse permitting electron pulse through.

While dilated electron pulse enters collimator, input electrode begins negative collimation pulse. output electrode grounded, creating time-varying acceleration field between electrodes collimator. electron pulse synchronized falling collimation pulse, which undergoes acceleration process. energy increase electrons behind lower energy greater electrons front higher energy. employing appropriate slope collimation pulse, ensure electrons nearly energy while achieve input surface. collimation pulse cathode pulse temporally delayed, delay being approximately equal flight electrons drift region.

Since input electrode begins loading collimation pulse electron pulse about reach collimator, impact collimation pulse movement electron pulse drift region almost negligible.

Furthermore, electron pulse passes through collimator picoseconds before entering grounded input surface

shield, having almost effect electron multiplication process within Therefore, employing collimation technique electron energy compensation improve uniformity without generating measurement errors. cathode pulses applied microstrip collimation pulse loaded collimator generated high-voltage pulse generator. generator comprises avalanche transistor pulse circuit field-effect transistor (FET) negative high-voltage pulse circuit. cascaded avalanche transistor employed produce fast-leading ultrafast pulse, which serves cathode pulse. circuit structure composed utilized generate negative high-voltage pulse, which collimation pulse.

While electron pulse output collimator, their energy nearly uniform. electron pulse subsequently enters electron multiplication. multiplied electrons accelerated toward anode electron detector electric field between output surface anode electron detection system, which includes anode electron detector high-speed oscilloscope, designed detect electron pulses amplified electric field between anode accelerates electron pulse toward anode, achieves nducing charges anode generates induced current output circuit. waveform output ultrafast current pulse recorded high-speed oscilloscope. anode electron detection system comprises anode, circuit, energy storage capacitors output circuit. circuit including high-voltage power supply current-limiting resistance applies voltage anode voltage creates acceleration field between

anode, charging energy storage capacitors energy storage capacitors store energy charge compensate energy losses induced current during operation anode electron detector.

Furthermore, capacitor isolates voltage high-speed oscilloscope, ensuring applied solely anode protecting oscilloscope.

Concurrently, capacitor short circuit high-frequency induced current signals, channeling downward-flowing induced current high-speed oscilloscope. anode constructed three microstrip transmission lines fabricated frequency printed circuit board.

These lines measure length, width, thickness, spaced apart shown Which electron pulse accelerated toward anode pulse current induced anode. pulse current propagates upward downward anode consistent waveforms. prevent upward-propagating pulse current reflecting causing oscillations pulse voltage waveform oscilloscope, resistor absorb upward-propagating pulse current. downward-propagating pulse current transmitted high-speed oscilloscope output circuit, which consists tapered transmission line, vacuum connector, coaxial cable.

Owing different impedances between anode connector, tapered transmission required between anode connector ensure impedance matching during transmission pulse current, thereby reducing attenuation pulse current. connector transfers pulse signal vacuum chamber outside delivers high-speed oscilloscope coaxial cable pulse waveform recording. induced current anode maintains impedance matching, oscilloscope obtain

almost undistorted waveform induced current. electron pulse temporally dilated, drift diagnostic system achieve temporal resolution lower temporal-resolution anode electron detector.

Owing large transmission distance drift region, electron pulse experiences radial space divergence. obtain electron pulse diameter collimator, magnetic image electron pulse microstrip collimator imaging ratio

3 Theoretical

research anode electron detector, electrons accelerated toward anode electric field while through transit electrons between anode expressed

� 푚� =

where represents distance between anode, represents charge electron, represents voltage applied represents voltage applied output surface, represents energy electron exits represents electron, represents voltage applied anode.

Equivalent ircuit lectron etection ystem; Relationship between temporal resolution anode electron detector voltage difference between anode leading anode output pulse depends transit electrons, whereas trailing depends discharge constant discharge circuit. oscilloscope's equivalent resistance which equal absorption resistance anode equivalent capacitor anode thus, anode electron detection system equivalent circuit shown discharge constants circuit, which composed anode given

� = 0.5 � �

�푛��� equivalent capacitance anode between anode could expressed

� �푛��� =

where represents dielectric constant, which vacuum. relative between anode electrostatic force constant, distance between anode.

discharge circuit

� �� = 2.75 � ( 4 )

temporal resolution anode electron detector �푛��� = 0.5 temporal resolution anode electron detector simulated. simulation anode spaced apart, voltage energy storage capacitor anode dimensions length width, absorption resistor thickness channel diameter slant angle input surface grounded output surface voltage spaced While discharge capacitance connected relationship between temporal resolution anode electron detector voltage difference between anode depicted temporal resolution increases increasing voltage difference. anode voltage increases increasing voltage difference between anode which improves temporal resolution anode electron detector While discharge capacitances separately temporal resolution anode electron detector varies voltage difference shown curves respectively.

Furthermore, smaller discharge capacitance higher temporal resolution. voltage difference, capacitance theoretical temporal resolution further improve temporal resolution, electron pulse time-dilation collimation system drift diagnostic system. temporal dilation factor

electron pulse time-dilation system simulated. temporal dilation factor mainly determined voltage, rising slope cathode pulse, electron drift region length electron pulse time-dilation achieved energy dispersion.

While linear cathode pulse used, electron energy change linearly.

Then, electron velocity change nonlinearly, resulting nonlinear temporal dilation electron pulse width. improve measured accuracy curved pulse necessary drive microstrip achieve linear change electron velocity resulting linear temporal dilation. ieving

result

cathode pulse temporal dilation factor slope position While microstrip applied curved cathode pulse rising slope starting point voltage shown position times electron pulse temporal dilation factors.

While rising slope used, temporal dilation factors improved times.

Cathode pulse rising profiles temporal dilation factors 50:1; Collimated pulse falling profiles temporal dilation factors electron pulse reaches collimator, temporal width magnified. collimator's input electrode applied collimation pulse, depicted

resulting electrons having energy while passing through collimator. falling slopes starting point respectively times times temporal dilation. temporal resolution drift diagnostic system varying cathode pulse slope simulated.

Here, anode electron detector temporal resolution simulation.

While microstrip loaded voltage cathode pulse, relationship between theoretical temporal resolution drift diagnostic system rising slope cathode pulse depicted slope increases larger V/ps, temporal resolution improves better While cathode pulse slope further increased greater V/ps,

temporal resolution will be significantly improved to better than 5 ps.

start point

results

drift diagnostic system developed, temporal resolution measured. temporal resolution measurement employs Michelson interferometer method, schematic diagram measurement setup shown laser outputting ultraviolet pulse wavelength width split beams semi-reflective passes through photodiode (PIN2) output electrical pulse, which high-speed oscilloscope monitor intensity ultraviolet laser trigger jitter between ultraviolet laser cathode pulse. other ultraviolet laser firstly reflected total reflection mirror reaches Michelson interferometer comprising semi-reflective total reflection mirrors resulting achieving light pulses adjustable intervals. light pulses sequentially reflected total reflection mirror attenuated neutral grayscale mirror attenuated light pulse expanded concave diameter about input microstrip directed photodiode generate trigger signal which delayed trigger high-voltage pulse generator produce pulses.

Three

athode pulses, other oscilloscope monitor trigger jitter between ultraviolet laser cathode pulse. circuit delay adjusted synchronize arrival light pulse cathode pulse microstrip electron pulse's temporal width dilated. state referred electron pulse dilation drift diagnostic system. ultrafast pulse signal output system detected high-speed oscilloscope. mirror fixed, mirror mounted high-precision displacement stage adjust position, thereby adjusting interval between light pulses. interval between light pulses larger system's temporal resolution, oscilloscope output electrical pulse pulse peaks. reducing optical difference, system's temporal resolution obtained according Rayleigh criterion. microstrip biased voltage without cathode pulse, drift diagnostic system works electron pulse non-dilation mode, allowing measurement temporal resolution anode electron detector. microstrip biased voltage without cathode pulse, electron pulse undergo temporal dilation. anode output electrical pulse waveform, detected oscilloscope, depicted which shows pulse width approximately Consequently, without electron pulse -dilation technology, system's temporal resolution measured approximately which temporal resolution anode electron detector.

Anode output electrical pulse waveform without electron pulse time-dilation technology; electrical pulse waveform output system while electron pulse time-dilation technology employed, optical pulses synchronized approximately relative starting cathode pulse, equivalent voltage about

experiment

measuring temporal resolution drift diagnostic system being electron pulse dilation mode, microstrip biased voltage cathode pulse rising slope V/ps, optical pulses interval Michelson interferometer enter system simultaneously.

While optical pulses synchronized approximately relative starting cathode pulse, diagnostic system dilates optical pulses, output electrical pulse waveform shown interval optical pulses magnified which achieved temporal dilation factor approximately times employing electron pulse time-dilation technology.

Schematic diagram input signal reconstruction algorithm based electron pulse temporal dilation factor interval between points pulse signal recorded oscilloscope, voltage value certain moment pulse signal. respectively represent three steps input signal reconstruction algorithm; cathode pulse pulse dilation electron pulse temporal dilation function D(t); Relationship between normalized electron energy; function experiment, photoelectrons converted input signal undergo series processes within drift diagnostic system, including electron pulse temporal dilation gain, generation pulsed current anode followed output. input signal reconstructed using detected electrical pulse signals, electron pulse temporal dilation function D(t), function G(t). input signal reconstruction algorithm comprises following three steps, illustrated Firstly, interval

between points pulse signal recorded oscilloscope divided electron pulse temporal dilation factor while vertical coordinate voltage value unchanged, thereby compressing pulse signal scale input signal without temporal dilation Secondly, voltage value point time-compressed pulse signal multiplied electron pulse temporal dilation factor Finally, voltage value point pulse signal obtained second divided obtaining input signal waveform.

While cathode pulse shown curve employed, electron pulse temporal dilation function derived electron pulse temporal dilation model illustrated curve electron energy gradually diminishes increases electron pulse temporal dilation, which leads decrease number secondary electrons produced electrons striking time.

Then, declined gradually. relationship between normalized electron energy measured, depicted energy electrons emitted different times while reach obtained Consequently, function achieved shown Using input signal reconstruction algorithm depicted along electron pulse temporal dilation factor function function G(t), electrical pulse waveform output system reconstructed input signal waveform. action effectively compresses pulse original scale prior magnification, resulting input signal waveform displayed

Post-decompression, pulse widths measure respectively. result, implementation electron pulse time-dilation technology, temporal resolution drift diagnostic system enhanced superior resolution Furthermore, interval between input signal which difference optical pulses outputted Michelson interferometer.

5 Conclusion

paper presents drift diagnostic system exploit electron pulse time-dilation collimation. enhances temporal resolution employing temporal dilation system dilate electron pulse.

Then, temporal dilation electron pulse energy compensated collimation system Finally, dilated electron pulse measured anode electron detector.

Theoretical studies suggest anode electron detector temporal resolution approximately While cathode pulse slope excite microstrip drift system achieves temporal resolution

greater slope further increased greater V/ps, temporal resolution significantly improved better drift diagnostic system developed temporal resolution measured. input signal reconstruction algorithm studied. temporal resolution approximately diagnostic system demonstrated based experimental results.

Future research focus using curved cathode pulses achieve linear temporal dilation electron pulse applying electron pulse collimation technology compensate

electron energy and enhance MCP gain uniformity.

Acknowledgements supported Program National Natural Science Foundation China (Grant Nos.12575223, 12575252), National Laboratory Plasma Physics (Grant JCKYS2025212807), Guangdong Basic Applied Basic Research Foundation (Grant 2025A1515011820, 2024A1515011832), Shenzhen Science Technology Program (Grant JCYJ20240813141605008, JCYJ20240813141615021, JCYJ20230808105019039), Shenzhen University Pursuit Excellence Research Program (Grant 2023C007), Scientific Foundation Youth Scholars Shenzhen University (Grant 806-0000340618), Shenzhen Laboratory Photonics Biophotonics (Grant ZDSYS20210623092006020) availability support findings study available reasonable request.

Declarations Conflict interest authors conflicts disclose.

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