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報告書

グローブボックス窓板用火災対策シートの開発

川崎 浩平; 品田 健太; 岡本 成利; 影山 十三男; 江田 考志; 岡崎 日路; 鈴木 弘道; 山本 和也; 小田部 隼

JAEA-Technology 2020-025, 80 Pages, 2021/03

JAEA-Technology-2020-025.pdf:3.72MB

プルトニウム燃料第三開発室は、高速実験炉「常陽」及び高速増殖原型炉「もんじゅ」のMOX燃料製造を目的に昭和63年に運転を開始した施設であり、非密封の核燃料物質を大量に取り扱う大型のグローブボックスが設置された。これらのグローブボックス窓板には「使用施設等の位置、構造及び設備の基準に関する規則」の施行(平成25年12月)以降に設置するものを除き、アクリル(可燃性)が用いられている。グローブボックス内の火災に対しては、建設当初からハロゲン化物消火設備による自動消火システムを導入しているが、グローブボックスの外側からの火災に対して、アクリルの直接的な対策が課題であった。そのため、可能な限りグローブボックスの外側からの火災に対するグローブボックス窓板への影響を軽減する火災対策シートを開発、最終的には難燃性のシートを実装した。開発の着眼点は、不燃又は難燃シートに粘着材を塗布した複合材で不燃又は難燃性を有していること。また、使用環境(核燃料物質からのガンマ線、蛍光灯からの紫外線)で劣化が著しくないこと、グローブ作業での作業員の視認性を確保できる透明なシートであること等とした。これらの火災対策シートを貼り付けたアクリル板の火災損傷防止試験及び火災対策シートを用いた使用環境影響試験を行い、良好な結果を得た。一方、火災対策シートの貼り付け作業等における外部被ばくを低減する観点から、プルトニウム燃料技術開発センター内にワーキンググループを立ち上げ、施工試験等で効率的な施工を実現する方法を検討・試行し、作業の標準化を図り、基本手順書にまとめた。本報告書は、グローブボックス窓板用火災対策シートに係る火災損傷防止試験及び使用環境影響試験と、施工性試験等を通じて得られた知見を取りまとめたものである。

報告書

模擬廃棄物含有バナジウム添加ホウケイ酸ガラス試料の評価研究

永井 崇之; 岡本 芳浩; 塩飽 秀啓; 猪瀬 毅彦*; 佐藤 誠一*; 畠山 清司*; 廣野 和也*; 本間 将啓*; 小林 博美*; 高橋 友恵*; et al.

JAEA-Research 2018-007, 87 Pages, 2018/11

JAEA-Research-2018-007.pdf:61.21MB

本研究は、資源エネルギー庁の「放射性廃棄物の減容化に向けたガラス固化技術の基盤研究事業」における、高レベル放射性廃液の充填率を高められる原料ガラス組成の開発として実施した。候補組成であるバナジウム(V)添加ガラス原料カレットへ模擬高レベル放射性廃液を混合溶融して作製した模擬廃棄物ガラス試料を対象に、レーザアブレーション(LA)法ICP-AES分析, ラマン分光測定及び放射光XAFS測定により評価を実施した。

論文

Ultralow emittance beam production based on Doppler laser cooling and coupling resonance

野田 章*; 中尾 政夫*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; 想田 光*; 頓宮 拓*; 神保 光一*; Grieser, M.*; He, Z.*; et al.

Proceedings of 5th International Particle Accelerator Conference (IPAC '14) (Internet), p.28 - 33, 2014/07

Three-dimensional (3D) cooling of 40-keV $$^{24}$$Mg$$^+$$ ion beams with Doppler laser cooling and the coupling resonance has been demonstrated in the storage ring S-LSR of Kyoto University toward the production of ultralow-emittance beams, in other words, ultracold beams and so-called crystalline beams. So far, the transverse temperatures of 6 K and 2 K have been experimentally attained in the horizontal and vertical directions, respectively, at a low beam intensity of about $$10^4$$ ions in the ring. These temperatures are the lowest ever attained by laser cooling of ion beams. Systematic molecular dynamics simulations predict the realization of further lower temperatures, $$approx$$ 1 mK and $$approx$$ 0.1 K in the longitudinal and transverse directions, respectively, if the laser spot size and detuning are properly adjusted even with such a low laser power ($$approx$$ 10 mW) as utilized in the experiments at S-LSR. A 3D ordered state of the beam with 3D laser cooling is also predicted. Recent experimental achievements and latest simulation results are presented.

論文

イオン蓄積・冷却リングS-LSRでのMgイオンビームのレーザー冷却

野田 章*; 中尾 政夫*; 想田 光*; 頓宮 拓*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; 神保 光一*; Grieser, M.*; He, Z.*

Proceedings of 10th Annual Meeting of Particle Accelerator Society of Japan (インターネット), p.143 - 145, 2014/06

We have experimentally demonstrated transverse indirect laser cooling utilizing synchro-betatron resonance coupling in the ion accumulation cooler ring S-LSR. However, its efficiency was rather poor for relatively high beam intensity of $$10^7$$ ions in the ring due to beam heating by intra-beam scattering and its cooling time was as long as 100 s. By application of beam scraping and optimization of laser detuning together with equilibrium deceleration with the use of an induction accelerator, we could reach the lowest transverse temperatures ever attained by laser cooling as 7.0 K and 2.1 K for the horizontal and vertical directions, respectively. The prospect of generating an ultra-low-temperature beam and realizing beam crystallization will be discussed on the basis of the present result.

報告書

原子力緊急時支援・研修センターの活動(平成24年度)

佐藤 猛; 武藤 重男; 奥野 浩; 片桐 裕実; 秋山 聖光; 岡本 明子; 小家 雅博; 池田 武司; 根本内 利正; 斉藤 徹; et al.

JAEA-Review 2013-046, 65 Pages, 2014/02

JAEA-Review-2013-046.pdf:11.18MB

原子力機構は、指定公共機関として、国及び地方公共団体その他の機関に対し、災害対策又は武力攻撃事態等への対処において、防災業務計画及び国民保護業務計画に則り、技術支援をする責務を有している。原子力緊急時支援・研修センターは、緊急時には、専門家の派遣、防災資機材の提供、防護対策のための技術的助言等の支援活動を行う。また、平常時には、我が国の防災対応体制強化・充実のために、自らの訓練・研修の他、国、地方公共団体、警察、消防、自衛隊等の原子力防災関係者のための訓練・研修、原子力防災に関する調査研究及び国際協力を実施する。平成24年度においては、上記業務を継続して実施するとともに、国の原子力防災体制の抜本的見直しに対し、これまでに培った経験及び東京電力福島第一原子力発電所事故への対応を通じた教訓等を活かし、国レベルでの防災対応基盤の強化に向け、専門家として技術的な支援を行うとともに、当センターの機能の維持・運営及び国との連携を図った自らの対応能力強化などに取り組んだ。なお、福島事故への対応については、人的・技術的な支援活動の主たる拠点が福島技術本部に移行することとなったため、平成24年9月をもって終了した。

論文

Measurements of electron-induced neutrons as a tool for determination of electron temperature of fast electrons in the task of optimization laser-produced plasma ions acceleration

榊 泰直; 西内 満美子; 前田 祥太; 匂坂 明人; Pirozhkov, A. S.; Pikuz, T.; Faenov, A.*; 小倉 浩一; 深見 智代; 松川 兼也*; et al.

Review of Scientific Instruments, 85(2), p.02A705_1 - 02A705_4, 2014/02

 被引用回数:2 パーセンタイル:13.22(Instruments & Instrumentation)

高強度レーザーとプラズマの相互作用によるイオン発生において、電子特性の計測は不可欠である。そのため、様々な計測手法が提案されているが、今回我々は、光核中性子反応による中性子を計測することで、精度よく電子特性の計測を行う新規性の高い手法を提案する。この手法は、イオン加速エネルギー計測と共にピークパワー1$$times$$10$$^{21}$$W/cm$$^{2}$$のJ-KARENレーザーによって実証された。イオン加速エネルギーと本手法による計測結果は極めて相関をもつことがわかり、改良を重ねて行けば非常に良い計測器になり得ることがわかった。

論文

Simulation study on transverse laser cooling and crystallization of heavy-ion beams at the cooler storage ring S-LSR

百合 庸介; 大崎 一哉*; 岡本 宏巳*; He, Z.*; 想田 光*; 野田 章*; 中尾 政夫*; 頓宮 拓*; 神保 光一*

Proceedings of Workshop on Beam Cooling and Related Topics (COOL '13) (Internet), p.162 - 165, 2013/11

Efficient transverse laser cooling of a low-intensity heavy-ion beam has been recently accomplished experimentally by means of the resonant coupling method at the cooler storage ring S-LSR of Kyoto University. In parallel with the experimental effort, multi-dimensional laser cooling of the ion beam has been studied also numerically with the molecular dynamics (MD) simulation code in which the stochastic interaction between ions and laser photons is incorporated in order to search optimum laser-cooling conditions and verify the results of the experiment. The present MD result demonstrates that, in spite of the limited experimental conditions of the cooling laser such as low power, fixed frequency, and short cooling section, a three-dimensionally low-temperature beam of 40-keV $$^{24}$$Mg$$^+$$ can be obtained through resonant coupling at a low intensity of $$10^4$$ ions in the ring, which is consistent with the experimental result.

論文

Latest results of experimental approach to ultra-cold beam at S-LSR

野田 章*; 中尾 政夫*; 想田 光*; 頓宮 拓*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; 神保 光一*; Grieser, M.*; He, Z.*

Proceedings of Workshop on Beam Cooling and Related Topics (COOL '13) (Internet), p.157 - 161, 2013/11

We have tried to approach to the lowest attainable beam temperature with laser cooling of a 40-keV $$^{24}$$Mg$$^+$$ ion beam at a cooler storage ring S-LSR, which has a superperiodicity of six and is designed to be tough against resonant perturbation to the circulating beam. The capability of active indirect transverse laser cooling has been experimentally demonstrated with the use of the theoretically-proposed synchro-betatron resonance coupling scheme. For the reduction of beam heating due to intrabeam scattering, an additional scheme has been established to control the intensity of the circulating beam down to $$sim 10^4$$ ions by scraping the outskirt of the beam with the use of a horizontally-moving scraper, which could cool the horizontal and vertical beam temperature down to $$sim 20$$ K and $$sim 30$$ K, respectively, at an operation tune without horizontal-vertical (H-V) coupling. In the present paper, we would like to also present our recent results with H-V coupling in addition to longitudinal-horizontal coupling toward further reduction of the transverse beam temperature.

論文

Parameter optimization for multi-dimensional laser cooling of an ion beam in the storage ring S-LSR

He, Z.*; Wei, J.*; 大崎 一哉*; 岡本 宏巳*; 野田 章*; 中尾 政夫*; 想田 光*; 百合 庸介; 神保 光一*

Proceedings of 25th North American Particle Accelerator Conference (NA-PAC '13) (Internet), p.1298 - 1300, 2013/09

The power of the cooling laser currently available in a compact ion cooler ring S-LSR, Kyoto University, is quite limited for generating ultralow-temperature ion beams. Therefore, parameters of laser cooling should be carefully determined in order to approach the lowest possible temperature in the experiment. This paper mainly concerns optimization of laser-cooling parameters and prediction of a possible lower limit of beam temperature in S-LSR, based on systematic molecular dynamics simulations. The adiabatic capture process of the ion beam was introduced to prevent the emittance from blowing up during bunching. The spot size of the laser was optimized with the total laser power limited. An optimum solenoid field strength was obtained for three-dimensional cooling. The lowest beam temperature achievable in S-LSR was predicted by choosing the parameters optimized.

論文

Efficiency enhancement of indirect transverse laser cooling with synchro-betatron resonant coupling by suppression of beam intensity

想田 光*; 中尾 政夫*; 頓宮 拓*; 神保 光一*; 大崎 一哉*; 岡本 宏巳*; 百合 庸介; He, Z.*; Grieser, M.*; 野田 章*

Japanese Journal of Applied Physics, 52(3), p.030202_1 - 030202_4, 2013/03

 被引用回数:4 パーセンタイル:20.97(Physics, Applied)

The efficiency of indirect transverse laser cooling of a heavy-ion beam using synchro-betatron resonant coupling (SBRC) was improved by the reduction of the beam intensity through scraping the tail part of the beam. In order to measure the beam size at low beam intensity, a new scheme was established where the beam profile was determined from the beam survival ratio by changing the insertion position of a beam scraper. At a beam intensity of $$10^4$$ particles in the ring, the transverse cooling time of the beam was reduced to 1.2 s, and horizontal and vertical minimum beam sizes were 0.2 mm and 0.6 mm, corresponding to the beam temperatures of 20 K and 29 K, respectively. The cooling time was much improved compared with that of our previous experiment, 100 s at $$10^7$$ particles (Nakao et al.). The transverse temperature was comparable to that in other work (Madsen et al.), in spite of the limitation in the experimental conditions such as low laser power and short laser-cooling section. This suggests that the present SBRC scheme has a potential capacity for attaining a lower-temperature beam or even Coulomb crystallization.

論文

Approach to the low temperature state oriented for crystalline beam

野田 章*; 中尾 政夫*; 想田 光*; 頓宮 拓*; 神保 光一*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; Meshkov, I.*; Smirnov, A.*; et al.

Proceedings of 23rd Russian Particle Accelerator Conference (RuPAC 2012) (Internet), p.48 - 52, 2012/09

Various approaches to attaining low-temperature beams have been continued in the cooler storage ring S-LSR at Kyoto University. One-dimensional ordering of electron-cooled 7-MeV protons was realized with an abrupt longitudinal temperature jump from 2 K to 0.3 K at a particle number of around 2000. Laser cooling has been applied to 40-keV $$^{24}$$Mg$$^+$$ beams toward the realization of crystalline beams. For a coasting beam, the lowest longitudinal temperature of 3.6 K was attained at $$4 times 10^4$$ ions. The temperature was limited due to intra-beam scattering (IBS). On the other hand, the transverse temperature of the beam indirectly cooled through IBS was saturated at 500 K for $$2 times 10^7$$ ions. In order to cool the transverse direction further, synchro-betatron resonance coupling has been applied to a bunched Mg beam. The transverse temperature has been reduced to the order of $$10^1$$ K at the beam intensity of $$10^4$$ ions by the reduction of the beam intensity using a scraper.

報告書

原子力緊急時支援・研修センターの活動(平成23年度)

片桐 裕実; 奥野 浩; 岡本 明子; 池田 武司; 田村 謙一; 長倉 智啓; 中西 千佳; 山本 一也; 阿部 美奈子; 佐藤 宗平; et al.

JAEA-Review 2012-033, 70 Pages, 2012/08

JAEA-Review-2012-033.pdf:6.38MB

日本原子力研究開発機構は、災害対策基本法等に基づき「指定公共機関」に指定されており、国及び地方公共団体その他の機関に対し、災害対策又は武力攻撃事態等への対処に関して、技術支援をする責務を有している。原子力緊急時支援・研修センターは、緊急時には、全国を視野に入れた専門家の派遣、防災資機材の提供、防護対策のための技術的助言等の支援活動を行う。また、平常時には、我が国の防災対応体制強化・充実のために、自らの訓練・研修の他、国, 地方公共団体, 警察, 消防, 自衛隊等の原子力防災関係者のための実践的な訓練・研修並びに原子力防災に関する調査研究を実施する。平成23年度においては、上記業務を継続して実施するとともに、平成23年3月11日の東日本大震災により発生した東京電力福島第一原子力発電所の事故対応について、原子力機構が実施する人的・技術的な支援活動の拠点として、原子力緊急時支援・研修センターを機能させた。各部署と連携を取りながら原子力機構の総力を挙げて、国,地方公共団体の支援要請を受け、事業者が対応する復旧にかかわる技術的検討、住民保護のためのさまざまな支援活動や、特殊車両・資機材の提供を継続して実施した。

論文

スクレイパーを用いた横方向レーザー冷却効果の観測

想田 光*; 中尾 政夫*; 頓宮 拓*; 野田 章*; 神保 光一*; 大崎 一哉*; 岡本 宏巳*; 百合 庸介; Grieser, M.*; He, Z.*

Proceedings of 9th Annual Meeting of Particle Accelerator Society of Japan (インターネット), p.388 - 390, 2012/08

京都大学化学研究所のイオン蓄積・冷却リングS-LSRでは、シンクロ・ベータトロン共鳴によって重イオンビームの運動の進行方向と水平方向の振動を結合させ、レーザー冷却によって横方向を間接的に冷却する実験を進めている。冷却の過程において、粒子数が多い場合Intra-beam散乱による自己加熱作用によって冷却が阻害されるため、スクレイパーによってビーム外縁部の粒子を除去することによって冷却効率を高めている。このとき、2枚のスクレイパーを用い、1枚目のスクレイパーで粒子数を減らした後、2枚目のスクレイパーの挿入距離を変えてビームの残存率を測定することで、ビーム中心からの距離とその内側にある粒子の割合が得られ、この関係から冷却後のビームサイズを測定した。その結果、40keV $$^{24}$$Mg$$^+$$ビームについて、水平・鉛直ベータトロンチューン、及びシンクロトロンチューンがそれぞれ(2.074, 1.120, 0.072)、1枚目のスクレイパーをビーム中心から0.3mmまで挿入して粒子数を1$$times$$10$$^5$$まで減少させた条件で、水平方向ビームサイズが0.3mm、温度に換算して52Kまで冷却されていることを観測した。この時、ビームサイズが1/eになるまでの冷却時間は1.25秒であった。

論文

横方向間接レーザー冷却の効率化に向けた制御ビームスクレーピング

野田 章*; 中尾 政夫*; 想田 光*; 頓宮 拓*; 神保 光一*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; Grieser, M.*; He, Z.*

Proceedings of 9th Annual Meeting of Particle Accelerator Society of Japan (インターネット), p.72 - 74, 2012/08

Laser cooling of 40-keV Mg ion has been performed at S-LSR. Indirect transverse laser cooling of a bunched beam with the use of synchro-betatron resonance coupling (SBRC) has been experimentally indicated. However, it is not so efficient due to heating by intra-beam scattering for the ion number of 10$$^7$$. For attaining very low-temperature beam, it is inevitable to reduce the beam intensity without deterioration of beam detection signal. For this purpose, we have applied controlled scraping of a laser-cooled beam. After beam injection, the beam tail is cut off by a scraper moving in the horizontal direction and laser-cooled both in the longitudinal and horizontal directions with SBRC. Then, the horizontal beam size was measured with another scraper moving also in the horizontal direction. With this scheme, the beam intensity could be reduced from 10$$^7$$ to 10$$^5$$, which resulted in rather efficient indirect transverse laser cooling with the cooling time of about 1 sec.

論文

Observation of 2-component bunched beam signal with laser cooling

想田 光*; 中尾 政夫*; 野田 章*; 頓宮 拓*; 伊藤 清一*; 岡本 宏巳*; 百合 庸介; 神保 光一*; Grieser, M.*; He, Z.*

Proceedings of 3rd International Particle Accelerator Conference (IPAC '12) (Internet), p.397 - 399, 2012/05

The longitudinal temperature of 40 keV $$^{24}$$Mg$$^+$$ beams was measured through bunch length measurement during laser cooling at S-LSR. The bunch length was measured as time-domain signals from a pair of parallel-plate electrostatic pickups. Injected non-cooled beams gave a bunch length of 2.5 m and cooled beams had two components of broad and sharp distributions. The broad distribution had a longitudinal length of 2.2 m, which is close to that of the initial beam. The length of the sharp distribution shrunk to 0.25 m and is expected as a cooled part. The capture efficiency of cooling, which represents the ratio of particle numbers of the cooled part and the total particle number, varied with laser detuning. With a scanning range of 2 GHz, it was improved from 66% to 92%, while the bunch became longer by 10% with scanning. A new scheme for improving the capture efficiency will be applied to attain a strong signal from a low-current low-temperature beam.

論文

Challenge for more efficient transverse laser cooling for beam crystallization

野田 章*; 中尾 政夫*; 想田 光*; 頓宮 拓*; 伊藤 清一*; 岡本 宏巳*; 大崎 一哉*; 百合 庸介; 神保 光一*; Grieser, M.*; et al.

Proceedings of 3rd International Particle Accelerator Conference (IPAC '12) (Internet), p.394 - 396, 2012/05

Mg ion beams have been successfully laser-cooled both in longitudinal and transverse directions at S-LSR in ICR, Kyoto University. The cooling rate, however, is not strong enough to realize a crystalline beam due to heating from intra-beam scattering (IBS). Reduction of the beam intensity is inevitable to suppress this IBS effect, which, however, had resulted in poor S/N ratio for observation of the transverse beam size. We, therefore, describe a new beam-scraping scheme: The scheme selects out ions in the distribution tail of the transverse phase space, keeping the beam density in the core part by simultaneous application of multi-dimensional laser cooling and beam scraping. The strategy to realize the scheme effectively has been searched by combination of the beam experiments and computer simulations.

論文

Intrabeam scattering at low temperature range

Yu, P.*; He, Z.*; Wei, J.*; Sessler, A. M.*; 岡本 宏巳*; 百合 庸介

Proceedings of 1st International Particle Accelerator Conference (IPAC '10) (Internet), p.1943 - 1945, 2010/05

In the process of beam cooling, the main heating source is intra-beam scattering (IBS), in which Coulomb collisions among particles lead to a growth of the beam's 6D phase-space volume. The results of molecular dynamics simulations have shown an increase of heating rate as the temperature increases from absolute zero, then a peak in the heating rate, and subsequent decrease with increasing temperature. On the other hand, in the traditional IBS theory, heating rate increases monotonically as the temperature becomes lower and lower. In this paper, we attempt to extend the traditional IBS theory valid at high temperatures to relatively low temperature range, by including some many-body effects in the traditional IBS theory. In particular, we take into account the static and dynamic effect of the self-electromagnetic field of the beam. We shall show how these effects modify the traditional theory, and present the evaluation of IBS heating rate of an ion beam in the low temperature range.

論文

Status and challenges in beam crystallization

Wei, J.*; Yu, P.*; 岡本 宏巳*; 百合 庸介; Li, X.-P.*; Sessler, A. M.*

Proceedings of Workshop on Beam Cooling and Related Topics (COOL '09) (Internet), p.86 - 90, 2010/00

During the past several decades, beam crystallization has been studied both theoretically and experimentally. Theoretical investigations have been numerical, mainly using computer modeling based on the method of molecular dynamics, and analytical, based on phonon theory. Experimental investigations involve both ion storage rings and ion traps using both electron and laser beam cooling. Topics of interests include crystal stability in various accelerator lattices and under different beam conditions, crystalline beam formation in shear-free ring lattices with both magnets and electrodes, experimental simulation of alternating-gradient conditions with an ion trap, etc. In this paper, we first review theoretical approaches and major conclusions pertaining to beam crystallization. Then, we analyze conditions and methods of the various major experiments. Finally, we discuss, both theoretically and experimentally, some improvements, open questions, and challenges in beam crystallization.

論文

Simulation study of emittance growth from Coulomb collisions in low-temperature ion beams

百合 庸介; 岡本 宏巳*; 杉本 寛*

Journal of the Physical Society of Japan, 78(12), p.124501_1 - 124501_10, 2009/12

 被引用回数:1 パーセンタイル:11.58(Physics, Multidisciplinary)

The collisional heating process of highly space-charge-dominated coasting ion beams in a storage ring was systematically investigated using the molecular dynamics simulation technique. To evaluate the heating rate over the whole temperature range, the simulation was started from an ultra-low-emittance state where the beam is Coulomb crystallized. When the ring is properly designed, the heating rate is quite low at ultralow temperature because random Coulomb collisions are suppressed. It gradually increases during the melting process of a Coulomb crystal and eventually comes to a peak at relatively low temperature where the beam is in a liquid phase. The dependence of the heating behavior is explored on various machine and beam parameters, such as the line density, betatron tune, kinetic energy, and mass number of ions. An approximate formula is given to estimate the magnitude of emittance at which the collisional heating is maximized.

論文

Coulomb coupling and heating of charged particle beams in the presence of dispersion

岡本 宏巳*; 杉本 寛*; 百合 庸介

Journal of Plasma and Fusion Research SERIES, Vol.8, p.950 - 954, 2009/09

We study the heating of space-charge-dominated coasting beams circulating in a storage ring. A number of molecular dynamics simulations are performed systematically to figure out the parameter-dependence of the heating rate due to interparticle Coulomb collisions. We introduce a new definition of the Coulomb coupling constant $$Gamma$$ that characterizes the phase of one-component plasmas. The new $$Gamma$$ is based on observable quantities and can be applied to dispersive situations. It is confirmed that the heating rate comes to a peak when the beam is in a liquid phase; the peak is always located at $$Gamma approx 1$$ regardless of particle species, beam energy, the strength of external confinement forces, and line density.

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