{"id":282042,"date":"2016-09-20T02:00:00","date_gmt":"2016-09-19T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=11d6e5f499c0a664741cf4cfccfcbc58"},"modified":"2016-09-20T02:00:00","modified_gmt":"2016-09-19T23:00:00","slug":"a-simple-derivation-for-amplitude-and-time-period-of-charged-particles-in-an-electrostatic-bathtubpotential","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=282042","title":{"rendered":"A simple derivation for amplitude and time period of charged particles in an electrostatic bathtub\r\npotential"},"content":{"rendered":"<p>An \u2018electrostatic bathtub potential\u2019 is defined and analytical expressions for the time period and<br \/>\namplitude of charged particles in this potential are obtained and compared with simulations. These<br \/>\nkinds of potentials are encountered in linear electrostatic ion traps, where the potential along the<br \/>\naxis appears like a bathtub. Ion traps are used in basic physics research and mass spectrometry to<br \/>\nstore ions; these stored ions make oscillatory motion within the confined volume of the trap.<br \/>\nUsually these traps are designed and studied using ion optical software, but in this work the<br \/>\nbathtub potential is reproduced by making two simple modifications to the harmonic oscillator<br \/>\npotential. The addition of a linear \u2018 k 1 | x |\u2019 potential makes the simple harmonic potential curve<br \/>\nsteeper with a sharper turn at the origin, while the introduction of a finite-length zero potential<br \/>\nregion at the centre reproduces the flat region of the bathtub curve. This whole exercise o&#8230;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>An \u2018electrostatic bathtub potential\u2019 is defined and analytical expressions for the time period and<br \/>\namplitude of charged particles in this potential are obtained and compared with simulations. These<br \/>\nkinds of potentials are encountered in linear el&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-282042","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/282042","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=282042"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/282042\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=282042"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=282042"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=282042"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}