Complete electromagnetic multipole expansion including toroidal moments

Saved in:

Bibliographic Details
Main Author:	A. Góngora T.
Format:	Artículo científico
Language:	en
Published:	Sociedad Mexicana de Física A.C. 2006
Subjects:	Física, Astronomía y Matemáticas electric multipole expansion Electromagnetic radiation magnetic and toroidal moments
Online Access:	Acceder al recurso
Tags:	Add Tag No Tags, Be the first to tag this record!

_version_	1866811751197048832
author	A. Góngora T.
author_facet	A. Góngora T.
contents	Complete electromagnetic multipole expansion including toroidal moments A. Góngora T. E. Ley-Koo Física, Astronomía y Matemáticas electric multipole expansion Electromagnetic radiation magnetic and toroidal moments The electromagnetic multipole expansion presented in this paper is complete on two accounts: i) It is valid for all points in space, and ii) it recognizes the existence of toroidal moments. The electromagnetic field due to alternating poloidal currents in a toroidal solenoid is evaluated exactly via the solution of the inhomogeneous vector Helmholtz equations, using the outgoing wave Green function technique and the Debye potentials for sources and fields. The physical meaning of the toroidal moments can be appreciated when they are compared with the familiar electric and magnetic moments; the analysis of the long-wavelength limit of the exact results also explains the previous neglect of the toroidal moments. The magnetostatic limit and the point source limit are also physically and didactically interesting. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065613 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.52
format	Artículo científico
id	redalyc_57065613
language	en
publishDate	2006
publisher	Sociedad Mexicana de Física A.C.
spellingShingle	Complete electromagnetic multipole expansion including toroidal moments A. Góngora T. Física, Astronomía y Matemáticas electric multipole expansion Electromagnetic radiation magnetic and toroidal moments Complete electromagnetic multipole expansion including toroidal moments A. Góngora T. E. Ley-Koo Física, Astronomía y Matemáticas electric multipole expansion Electromagnetic radiation magnetic and toroidal moments The electromagnetic multipole expansion presented in this paper is complete on two accounts: i) It is valid for all points in space, and ii) it recognizes the existence of toroidal moments. The electromagnetic field due to alternating poloidal currents in a toroidal solenoid is evaluated exactly via the solution of the inhomogeneous vector Helmholtz equations, using the outgoing wave Green function technique and the Debye potentials for sources and fields. The physical meaning of the toroidal moments can be appreciated when they are compared with the familiar electric and magnetic moments; the analysis of the long-wavelength limit of the exact results also explains the previous neglect of the toroidal moments. The magnetostatic limit and the point source limit are also physically and didactically interesting. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065613 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.52
title	Complete electromagnetic multipole expansion including toroidal moments
topic	Física, Astronomía y Matemáticas electric multipole expansion Electromagnetic radiation magnetic and toroidal moments
url	https://www.redalyc.org/articulo.oa?id=57065613

if (filemtime($filename) + $maxlifetime < time()) { unlink($filename); $count++; } } return $count; } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ protected function saveSession($sessId, $data): bool { $sessFile = $this->path . '/sess_' . $sessId; if ($handle = fopen($sessFile, 'w')) { $return = false; // Lock the file for exclusive access to avoid issues with multiple // processes writing session simultaneously: if (flock($handle, LOCK_EX)) { $return = fwrite($handle, $data); // Make sure that there's no trailing data by truncating the file to // the correct length: ftruncate($handle, strlen($data)); fflush($handle); flock($handle, LOCK_UN); } fclose($handle); if ($return !== false) { return true; } } // If we got this far, something went wrong with the file output... // It is tempting to throw an exception here, but this code is called // outside of the context of exception handling, so all we can do is // echo a message.

// Anecdotal testing Today and Yesterday seems to indicate destroy() // is called by the garbage collector and everything is good. // Something to keep in mind though. return 0; } /** * Write function that is called when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ public function write($sessId, $data): bool { if ($this->writesDisabled) { return true; } return $this->saveSession($sessId, $data); } /** * A function that is called internally when session data is to be saved. * * @param string $sessId The current session ID * @param string $data The session data to write * * @return bool */ abstract protected function saveSession($sessId, $data): bool; }

* * @return void */ public function writeClose() { // The assumption is that we're using PHP's ext/session. // session_write_close() will actually overwrite $_SESSION with an // empty array on completion -- which leads to a mismatch between what // is in the storage object and $_SESSION. To get around this, we // temporarily reset $_SESSION to an array, and then re-link it to // the storage object. // // Additionally, while you _can_ write to $_SESSION following a // session_write_close() operation, no changes made to it will be // flushed to the session handler. As such, we now mark the storage // object isImmutable. $storage = $this->getStorage(); if (! $storage->isImmutable()) { $_SESSION = $storage->toArray(true); session_write_close(); $storage->fromArray($_SESSION); $storage->markImmutable(); } } /** * Attempt to set the session name * * If the session has already been started, or if the name provided fails * validation, an exception will be raised. * * @param string $name * @return SessionManager * @throws Exception\InvalidArgumentException */ public function setName($name) { if ($this->sessionExists()) { throw new Exception\InvalidArgumentException( 'Cannot set session name after a session has already started'

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"6bc5b3cb6bb4dd1320c7708c433711a9"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1789458833.197 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "6bc5b3cb6bb4dd1320c7708c433711a9" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1455}
SessionHelper	Laminas\Stdlib\ArrayObject {#1785}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=6bc5b3cb6bb4dd1320c7708c433711a9"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.61"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"38428"
REDIRECT_URL	"/Record/redalyc_57065613/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/redalyc_57065613/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1789458833.1909
REQUEST_TIME	1789458833

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Environment & details:

GET Data empty

POST Data empty

Files empty

Key	Value
ui	"standard"
language	"en"
VUFIND_SESSION	"6bc5b3cb6bb4dd1320c7708c433711a9"

Session

Key	Value
__Laminas	array:2 [`"_REQUEST_ACCESS_TIME" => 1789458833.197 "_VALID" => array:1 [ "Laminas\Session\Validator\Id" => "6bc5b3cb6bb4dd1320c7708c433711a9" ]`]
SessionState	Laminas\Stdlib\ArrayObject {#938}
FlashMessenger	Laminas\Stdlib\ArrayObject {#1455}
SessionHelper	Laminas\Stdlib\ArrayObject {#1785}

Server/Request Data

Key	Value
REDIRECT_VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
REDIRECT_HTTPS	"on"
REDIRECT_SSL_TLS_SNI	"info.umar.mx"
REDIRECT_STATUS	"200"
VUFIND_LOCAL_DIR	"/usr/local/vufind/local"
HTTPS	"on"
SSL_TLS_SNI	"info.umar.mx"
HTTP_ACCEPT	"/"
HTTP_USER_AGENT	"Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)"
HTTP_COOKIE	"ui=standard; language=en; VUFIND_SESSION=6bc5b3cb6bb4dd1320c7708c433711a9"
HTTP_ACCEPT_ENCODING	"gzip, br, zstd, deflate"
HTTP_HOST	"info.umar.mx"
PATH	"/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin:/snap/bin"
SERVER_SIGNATURE	"<address>Apache/2.4.66 (Ubuntu) Server at info.umar.mx Port 443</address>\n"
SERVER_SOFTWARE	"Apache/2.4.66 (Ubuntu)"
SERVER_NAME	"info.umar.mx"
SERVER_ADDR	"200.23.222.19"
SERVER_PORT	"443"
REMOTE_ADDR	"216.73.216.61"
DOCUMENT_ROOT	"/usr/local/vufind/public"
REQUEST_SCHEME	"https"
CONTEXT_PREFIX	""
CONTEXT_DOCUMENT_ROOT	"/usr/local/vufind/public"
SERVER_ADMIN	"admin@localhost"
SCRIPT_FILENAME	"/usr/local/vufind/public/index.php"
REMOTE_PORT	"38428"
REDIRECT_URL	"/Record/redalyc_57065613/Details"
GATEWAY_INTERFACE	"CGI/1.1"
SERVER_PROTOCOL	"HTTP/1.1"
REQUEST_METHOD	"GET"
QUERY_STRING	""
REQUEST_URI	"/Record/redalyc_57065613/Details"
SCRIPT_NAME	"/index.php"
PHP_SELF	"/index.php"
REQUEST_TIME_FLOAT	1789458833.1909
REQUEST_TIME	1789458833

Environment Variables empty

Registered Handlers

0. Whoops\Handler\PrettyPageHandler

Similar Items

Environment & details:

Environment & details: