{"id":3660,"date":"2026-08-30T00:24:17","date_gmt":"2026-08-29T16:24:17","guid":{"rendered":"https:\/\/blog.zengqq.com.cn\/?p=3660"},"modified":"2026-08-30T00:38:24","modified_gmt":"2026-08-29T16:38:24","slug":"%e5%9f%ba%e4%ba%8e%e5%8f%8d%e5%90%91%e4%bc%a0%e6%92%ad%e7%ae%97%e6%b3%95%e7%9a%84linac%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e8%b0%83%e4%bc%98%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/blog.zengqq.com.cn\/?p=3660","title":{"rendered":"\u57fa\u4e8e\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684linac\u4eba\u5de5\u667a\u80fd\u8c03\u4f18\u7b97\u6cd5"},"content":{"rendered":"\n

\u591a\u7ea7 Linac \u8c03\u8c10\u4e0e\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u7c7b\u6bd4\uff1a\u4ece Phase \/ Amplitude Tuning \u5230 Gradient Optimization<\/h1>\n\n\n\n

\u5173\u952e\u8bcd\uff1a<\/strong>Linac\u3001Linear Accelerator\u3001RF Phase\u3001Amplitude\u3001Beam Tuning\u3001Gradient Optimization\u3001Backpropagation\u3001Coordinate Descent\u3001SPSA\u3001Accelerator Physics\u3001first author: Qing-qi zeng (qing-qi.zeng@st.com)<\/p>\n\n\n\n

\n\n\n\n

\u6458\u8981<\/h2>\n\n\n\n

\u5728\u591a\u7ea7 Linac\uff08Linear Accelerator\uff09\u7cfb\u7edf\u4e2d\uff0c\u4e3a\u4e86\u4f7f\u524d\u4e00\u7ea7\u52a0\u901f\u540e\u7684\u79bb\u5b50\u80fd\u591f\u88ab\u540e\u4e00\u7ea7 Linac \u6709\u6548\u63a5\u53d7\u5e76\u7ee7\u7eed\u83b7\u5f97\u52a0\u901f\uff0c\u5de5\u7a0b\u4e0a\u901a\u5e38\u9700\u8981\u5bf9\u6bcf\u4e00\u7ea7 Linac \u7684 RF Phase<\/strong> \u548c Amplitude<\/strong> \u8fdb\u884c\u8c03\u8282\u3002 \u5b9e\u9645\u8c03\u8bd5\u8fc7\u7a0b\u4e2d\uff0c\u4e00\u4e2a\u5e38\u89c1\u7684\u65b9\u6cd5\u662f\u6539\u53d8\u67d0\u4e00\u7ea7 Linac \u7684 Phase\uff0c\u4f8b\u5982\u589e\u52a0\u6216\u51cf\u5c11\u4e00\u4e2a\u5c0f\u7684\u6b65\u957f\uff0c\u7136\u540e\u89c2\u5bdf\u6700\u7ec8 Beam \u7684\u53d8\u5316\u3002 \u5982\u679c Beam \u589e\u5927\uff0c\u5219\u8ba4\u4e3a\u5f53\u524d\u8c03\u8282\u65b9\u5411\u662f\u6b63\u786e\u7684\uff0c\u5e76\u7ee7\u7eed\u5411\u8be5\u65b9\u5411\u4f18\u5316\u3002<\/p>\n\n\n\n

\u8fd9\u79cd\u8c03\u8282\u65b9\u5f0f\u4ece\u601d\u60f3\u4e0a\u4e0e\u673a\u5668\u5b66\u4e60\u4e2d\u7684 Gradient-based Optimization<\/strong> \u4ee5\u53ca Backpropagation<\/strong> \u5b58\u5728\u660e\u663e\u7684\u76f8\u4f3c\u6027\uff1a\u7cfb\u7edf\u5e76\u4e0d\u76f4\u63a5\u6839\u636e\u67d0\u4e00\u7ea7 Linac \u7684\u5c40\u90e8\u72b6\u6001\u5224\u65ad\u53c2\u6570\u662f\u5426\u6700\u4f18\uff0c\u800c\u662f\u901a\u8fc7\u6700\u7ec8 Output \u7684\u53d8\u5316\u53cd\u5411\u5224\u65ad\u524d\u7ea7\u53c2\u6570\u7684\u8c03\u6574\u65b9\u5411\u3002<\/p>\n\n\n\n

\u7136\u800c\uff0c\u771f\u5b9e Linac \u7cfb\u7edf\u901a\u5e38\u662f\u4e00\u4e2a\u590d\u6742\u7684\u7269\u7406\u9ed1\u76d2\u7cfb\u7edf\uff0c\u5de5\u7a0b\u5e08\u65e0\u6cd5\u76f4\u63a5\u83b7\u5f97\u5b8c\u6574\u7684\u89e3\u6790\u68af\u5ea6\uff0c\u56e0\u6b64\u8fd9\u79cd\u5b9e\u9645\u8c03\u8282\u8fc7\u7a0b\u4e25\u683c\u6765\u8bf4\u5e76\u4e0d\u662f Neural Network \u4e2d\u7684 Backpropagation\u3002 \u5b83\u66f4\u63a5\u8fd1\u4e8e Black-box Optimization\u3001Finite Difference Gradient Estimation\u3001Hill Climbing<\/strong> \u548c Coordinate Descent<\/strong> \u7b49\u4f18\u5316\u65b9\u6cd5\u3002<\/p>\n\n\n\n

\u672c\u6587\u5c1d\u8bd5\u5efa\u7acb\u4e00\u4e2a\u7b80\u5316\u7684\u6570\u5b66\u6a21\u578b\uff0c\u5c06\u591a\u7ea7 Linac \u4e0e Neural Network \u7684 Layer-by-Layer \u7ed3\u6784\u8fdb\u884c\u7c7b\u6bd4\uff0c\u5e76\u8fdb\u4e00\u6b65\u8ba8\u8bba\u8fd9\u79cd\u7c7b\u6bd4\u662f\u5426\u80fd\u591f\u7528\u4e8e\u6784\u5efa\u81ea\u52a8\u5316 Linac Tuning \u7b97\u6cd5\u3002<\/p>\n\n\n\n

1. \u591a\u7ea7 Linac \u7cfb\u7edf\u7684\u57fa\u672c\u6a21\u578b<\/h2>\n\n\n\n

\u5047\u8bbe\u7cfb\u7edf\u7531 n \u4e2a Linac<\/strong> \u4e32\u8054\u7ec4\u6210\uff1a<\/p>\n\n\n\n

Ion Source\n    \u2502\n    \u25bc\nLinac 1 \u2500\u2500 Phase\u2081 \/ Amplitude\u2081\n    \u2502\n    \u25bc\nLinac 2 \u2500\u2500 Phase\u2082 \/ Amplitude\u2082\n    \u2502\n    \u25bc\nLinac 3 \u2500\u2500 Phase\u2083 \/ Amplitude\u2083\n    \u2502\n    \u25bc\n   ...\n    \u2502\n    \u25bc\nLinac n \u2500\u2500 Phase\u2099 \/ Amplitude\u2099\n    \u2502\n    \u25bc\nFinal Beam\n  <\/pre>\n\n\n\n
\u5b9a\u4e49\u7b2c i \u7ea7 Linac \u7684\u8f93\u5165 Beam \u72b6\u6001\u4e3a\uff1a<\/p>\n\n\n\n
Beami<\/sub><\/strong><\/p>\n\n\n\n
\u8be5\u72b6\u6001\u7ecf\u8fc7\u7b2c i \u4e2a Linac \u540e\u5f62\u6210\uff1a<\/p>\n\n\n\n
Beami+1<\/sub> = fi<\/sub>(Beami<\/sub>, \u03c6i<\/sub>, Ai<\/sub>)<\/strong><\/p>\n\n\n\n
\u5176\u4e2d\uff1a<\/p>\n\n\n\n
    \n
  • Beami<\/sub><\/strong>\uff1a\u8fdb\u5165\u7b2c i \u4e2a Linac \u7684 Beam \u72b6\u6001\uff1b<\/li>\n\n\n\n
  • \u03c6i<\/sub><\/strong>\uff1a\u7b2c i \u4e2a Linac \u7684 RF Phase\uff1b<\/li>\n\n\n\n
  • Ai<\/sub><\/strong>\uff1a\u7b2c i \u4e2a Linac \u7684 RF Amplitude\uff1b<\/li>\n\n\n\n
  • fi<\/sub><\/strong>\uff1a\u7b2c i \u4e2a Linac \u5bf9 Beam \u7684\u5b9e\u9645\u7269\u7406\u4f5c\u7528\u3002<\/li>\n<\/ul>\n\n\n\n
    \u8fd9\u91cc\u7684\u4e00\u4e2a\u91cd\u8981\u7279\u70b9\u662f\uff1a Beami<\/sub> \u5728\u771f\u5b9e\u7cfb\u7edf\u4e2d\u901a\u5e38\u53ef\u4ee5\u901a\u8fc7 diagnostics \u6d4b\u91cf\u5f97\u5230\uff0c\u800c fi<\/sub> \u672c\u8eab\u53ef\u80fd\u975e\u5e38\u590d\u6742\uff0c\u751a\u81f3\u96be\u4ee5\u5efa\u7acb\u5b8c\u6574\u7684\u89e3\u6790\u6a21\u578b\u3002<\/strong><\/p>\n\n\n\n
    2. Phase \u4e0e Amplitude \u5bf9 Energy Gain \u7684\u5f71\u54cd<\/h2>\n\n\n\n
    \u5728\u4e00\u4e2a\u7b80\u5316\u7684 RF acceleration \u6a21\u578b\u4e2d\uff0c\u7b2c i \u4e2a Linac \u5bf9\u79bb\u5b50\u7684\u80fd\u91cf\u589e\u76ca\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
    \u0394Ei<\/sub> \u221d Ai<\/sub> sin(\u03c6i<\/sub>)<\/strong><\/p>\n\n\n\n
    \u8fd9\u91cc\u91c7\u7528\u7684\u662f\u4ee5\u7279\u5b9a RF phase convention \u5b9a\u4e49\u7684\u8868\u8fbe\u5f62\u5f0f\u3002 \u5982\u679c\u7cfb\u7edf\u5c06\u6700\u5927 accelerating field \u5b9a\u4e49\u5728 \u03c6 = 0\u00b0\uff0c\u5219\u540c\u6837\u7684\u5173\u7cfb\u53ef\u80fd\u5199\u6210 cos(\u03c6) \u7684\u5f62\u5f0f\u3002 \u56e0\u6b64\u5b9e\u9645\u5de5\u7a0b\u4e2d\u5fc5\u987b\u9996\u5148\u660e\u786e Phase Reference\u3002<\/p>\n\n\n\n
    \u5728\u7b80\u5316\u6a21\u578b\u4e0b\uff1a<\/p>\n\n\n\n
    Ei+1<\/sub> = Ei<\/sub> + ki<\/sub>Ai<\/sub>sin(\u03c6i<\/sub>)<\/strong><\/p>\n\n\n\n
    \u5176\u4e2d ki<\/sub> \u662f\u4e00\u4e2a\u7efc\u5408\u7cfb\u6570\uff0c\u7528\u4e8e\u63cf\u8ff0 RF structure\u3001effective length\u3001transit-time factor\u3001particle charge \u7b49\u56e0\u7d20\u3002<\/p>\n\n\n\n
    \u56e0\u6b64\u9700\u8981\u7279\u522b\u533a\u5206\u4e24\u4e2a\u6982\u5ff5\uff1a<\/p>\n\n\n\n
      \n
    • Energy Gain<\/strong> \u53ef\u4ee5\u5728\u7b80\u5316\u6761\u4ef6\u4e0b\u8fd1\u4f3c\u4e0e A sin(\u03c6) \u6210\u6b63\u6bd4\uff1b<\/li>\n\n\n\n
    • Beam Count \/ Transmission<\/strong> \u5e76\u4e0d\u7b80\u5355\u7b49\u4e8e A sin(\u03c6)\u3002<\/li>\n<\/ul>\n\n\n\n
      \u6700\u7ec8 Beam \u6570\u91cf\u8fd8\u53d7\u5230 phase-space\u3001acceptance\u3001capture\u3001energy distribution\u3001transmission \u7b49\u56e0\u7d20\u5f71\u54cd\u3002<\/p>\n\n\n\n
      3. \u4e3a\u4ec0\u4e48 Beami<\/sub> \u7684\u6d4b\u91cf\u975e\u5e38\u91cd\u8981<\/h2>\n\n\n\n
      \u5728\u771f\u5b9e accelerator \u4e2d\uff0c\u8fdb\u5165\u67d0\u4e00\u7ea7 Linac \u7684 Beam \u5e76\u4e0d\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u6807\u91cf\u3002 \u5b83\u53ef\u80fd\u5305\u542b\uff1a<\/p>\n\n\n\n
        \n
      • Particle Number<\/li>\n\n\n\n
      • Energy<\/li>\n\n\n\n
      • Energy Spread<\/li>\n\n\n\n
      • Longitudinal Phase<\/li>\n\n\n\n
      • Transverse Phase Space<\/li>\n\n\n\n
      • Beam Current<\/li>\n\n\n\n
      • Emittance<\/li>\n<\/ul>\n\n\n\n
        \u56e0\u6b64\u66f4\u5408\u7406\u7684\u8868\u8fbe\u65b9\u5f0f\u662f\uff1a<\/p>\n\n\n\n
        Beam\u1d62\n  \u2502\n  \u2502  Phase\u1d62 \/ Amplitude\u1d62\n  \u25bc\n\u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502     Linac i      \u2502\n\u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n  \u2502\n  \u25bc\nBeam\u1d62\u208a\u2081\n  <\/pre>\n\n\n\n
        Beami<\/sub> \u53ef\u4ee5\u901a\u8fc7 Beam Diagnostics \u6d4b\u91cf\uff0c\u800c Beami+1<\/sub> \u662f\u7ecf\u8fc7\u5f53\u524d Linac \u540e\u5f62\u6210\u7684\u65b0\u72b6\u6001\u3002 \u8fd9\u4f7f\u6574\u4e2a\u7cfb\u7edf\u5177\u6709\u660e\u663e\u7684\u4e32\u8054\u7ed3\u6784\u3002<\/p>\n\n\n\n
        4. \u4e00\u4e2a\u5b9e\u9645\u7684 Phase Tuning \u5b9e\u9a8c<\/h2>\n\n\n\n
        \u5047\u8bbe\u76ee\u524d\u6b63\u5728\u8c03\u8282\u7b2c\u4e09\u4e2a Linac\uff1a<\/p>\n\n\n\n
        Phase\u2083 = 20\u00b0\n  <\/pre>\n\n\n\n
        \u9996\u5148\u5c06 Phase \u589e\u52a0\u4e00\u4e2a\u5c0f\u6b65\u957f\uff1a<\/p>\n\n\n\n
        20\u00b0 \u2192 21\u00b0\n  <\/pre>\n\n\n\n
        \u5982\u679c\u6700\u7ec8 Beam \u4ece\uff1a<\/p>\n\n\n\n
        1000 \u2192 1080\n  <\/pre>\n\n\n\n
        \u5219\u53ef\u4ee5\u5224\u65ad\uff1a<\/p>\n\n\n\n
        \u5728\u5f53\u524d\u5de5\u4f5c\u70b9\u9644\u8fd1\uff0cPhase\u2083 \u5f80\u589e\u52a0\u65b9\u5411\u8c03\u6574\u662f\u6709\u5229\u7684\u3002<\/strong><\/p>\n\n\n\n
        \u518d\u5411\u53cd\u65b9\u5411\u6d4b\u8bd5\uff1a<\/p>\n\n\n\n
        20\u00b0 \u2192 19\u00b0\n  <\/pre>\n\n\n\n
        \u5982\u679c Beam \u53d8\u6210\uff1a<\/p>\n\n\n\n
        1000 \u2192 920\n  <\/pre>\n\n\n\n
        \u90a3\u4e48\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n
        Phase\u2083 \u589e\u5927\u7684\u65b9\u5411\u662f\u5f53\u524d\u5c40\u90e8\u533a\u57df\u5185\u7684\u6b63\u786e\u4f18\u5316\u65b9\u5411\u3002<\/strong><\/p>\n\n\n\n
        \u6570\u5b66\u4e0a\uff0c\u8fd9\u5b9e\u9645\u4e0a\u662f\u5728\u4f30\u8ba1\uff1a<\/p>\n\n\n\n
        \u2202J \/ \u2202\u03c63<\/sub><\/strong><\/p>\n\n\n\n
        \u5176\u4e2d J \u662f\u6700\u7ec8 Beam \u7684\u8bc4\u4ef7\u6307\u6807\u3002<\/p>\n\n\n\n
        5. \u8fd9\u4e3a\u4ec0\u4e48\u5f88\u50cf Backpropagation\uff1f<\/h2>\n\n\n\n
        Neural Network \u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
        Input
          \u2502
          \u25bc
        Layer 1
          \u2502
          \u25bc
        Layer 2
          \u2502
          \u25bc
        Layer 3
          \u2502
          \u25bc
        Output
          \u2502
          \u25bc
        Loss
          <\/pre>\n\n\n\n
        \u591a\u7ea7 Linac \u5219\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
        Beam\u2080\n  \u2502\n  \u25bc\nLinac 1\n  \u2502\n  \u25bc\nBeam\u2081\n  \u2502\n  \u25bc\nLinac 2\n  \u2502\n  \u25bc\nBeam\u2082\n  \u2502\n  \u25bc\nLinac 3\n  \u2502\n  \u25bc\n...\n  \u2502\n  \u25bc\nFinal Beam\n  <\/code><\/pre>\n\n\n\n
        \u4e24\u8005\u5177\u6709\u975e\u5e38\u660e\u663e\u7684\u7ed3\u6784\u5bf9\u5e94\u5173\u7cfb\uff1a<\/p>\n\n\n\n
        Neural Network<\/th>Linac System<\/th><\/tr><\/thead>
        Input<\/td>Initial Beam<\/td><\/tr>
        Layer<\/td>Linac<\/td><\/tr>
        Weight<\/td>Phase \/ Amplitude<\/td><\/tr>
        Activation \/ Transformation<\/td>RF Acceleration \/ Beam Dynamics<\/td><\/tr>
        Output<\/td>Final Beam<\/td><\/tr>
        Loss \/ Objective<\/td>Beam Target \/ Transmission \/ Particle Count<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
        \u6700\u91cd\u8981\u7684\u76f8\u4f3c\u6027\u5728\u4e8e\uff1a<\/p>\n\n\n\n
        \n
        \u6700\u7ec8 Output \u7684\u53d8\u5316\u53ef\u4ee5\u7528\u4e8e\u5224\u65ad\u524d\u9762\u53c2\u6570\u5e94\u8be5\u5411\u54ea\u4e2a\u65b9\u5411\u8c03\u6574\u3002<\/p>\n<\/blockquote>\n\n\n\n
        6. \u4f46\u5b83\u5e76\u4e0d\u662f\u771f\u6b63\u7684 Backpropagation<\/h2>\n\n\n\n
        \u867d\u7136\u601d\u60f3\u76f8\u4f3c\uff0c\u4f46\u4e8c\u8005\u5728\u6570\u5b66\u5b9e\u73b0\u4e0a\u5b58\u5728\u672c\u8d28\u533a\u522b\u3002<\/p>\n\n\n\n
        Neural Network \u7684 Backpropagation \u5229\u7528 Chain Rule\uff1a<\/p>\n\n\n\n
        \u2202L\/\u2202x = (\u2202L\/\u2202y)(\u2202y\/\u2202x)<\/strong><\/p>\n\n\n\n
        \u56e0\u6b64\u53ea\u8981\u6a21\u578b\u53ef\u5fae\uff0c\u5c31\u53ef\u4ee5\u4ece\u6700\u7ec8 Loss \u51fa\u53d1\uff0c\u8ba1\u7b97\u6bcf\u4e00\u5c42\u53c2\u6570\u7684 Gradient\u3002<\/p>\n\n\n\n
        \u800c\u5b9e\u9645 Linac \u8c03\u8282\u901a\u5e38\u662f\uff1a<\/p>\n\n\n\n
        \u6539\u53d8 Phase\n    \u2502\n    \u25bc\n\u771f\u5b9e Accelerator\n    \u2502\n    \u25bc\n\u6d4b\u91cf Beam\n    \u2502\n    \u25bc\nBeam \u589e\u5927\u8fd8\u662f\u51cf\u5c0f\uff1f\n    \u2502\n    \u25bc\n\u5224\u65ad\u4e0b\u4e00\u6b65\u65b9\u5411\n  <\/pre>\n\n\n\n
        \u5de5\u7a0b\u5e08\u5e76\u6ca1\u6709\u76f4\u63a5\u5f97\u5230\u5b8c\u6574\u7684\uff1a<\/p>\n\n\n\n
        \u2202J \/ \u2202\u03c6i<\/sub><\/strong><\/p>\n\n\n\n
        \u800c\u662f\u901a\u8fc7\u771f\u5b9e\u673a\u5668\u5b9e\u9a8c\u8fd1\u4f3c\u4f30\u8ba1\u5b83\u7684\u7b26\u53f7\u3002<\/p>\n\n\n\n
        \u4f8b\u5982\uff1a<\/p>\n\n\n\n
        J(\u03c6 + \u0394\u03c6) > J(\u03c6)\n\n        \u2193\n\n\u2202J\/\u2202\u03c6 > 0\n\n        \u2193\n\nPhase \u5e94\u8be5\u7ee7\u7eed\u589e\u52a0\n  <\/pre>\n\n\n\n
        7. Finite Difference\uff1a\u5b9e\u9645\u8c03\u8282\u672c\u8d28\u4e0a\u662f\u5728\u201c\u6d4b Gradient\u201d<\/h2>\n\n\n\n
        \u5982\u679c\u91c7\u7528\u6709\u9650\u5dee\u5206\u65b9\u6cd5\uff0c\u53ef\u4ee5\u5199\u6210\uff1a<\/p>\n\n\n\n
        \u2202J\/\u2202\u03c6i<\/sub> \u2248 [J(\u03c6i<\/sub> + \u0394\u03c6) – J(\u03c6i<\/sub>)] \/ \u0394\u03c6<\/strong><\/p>\n\n\n\n
        \u66f4\u7cbe\u786e\u7684\u4e2d\u5fc3\u5dee\u5206\u5f62\u5f0f\u4e3a\uff1a<\/p>\n\n\n\n
        \u2202J\/\u2202\u03c6i<\/sub> \u2248 [J(\u03c6i<\/sub> + \u0394\u03c6) – J(\u03c6i<\/sub> – \u0394\u03c6)] \/ 2\u0394\u03c6<\/strong><\/p>\n\n\n\n
        \u56e0\u6b64\uff0c\u5de5\u7a0b\u5e08\u901a\u8fc7\uff1a<\/p>\n\n\n\n
        Phase + \u0394\n    \u2193\nMeasure Beam\n\nPhase - \u0394\n    \u2193\nMeasure Beam\n\n        \u2193\n\nEstimate Gradient\n  <\/pre>\n\n\n\n
        \u5176\u5b9e\u5df2\u7ecf\u5728\u505a\u4e00\u79cd\u975e\u5e38\u539f\u59cb\u4f46\u771f\u5b9e\u6709\u6548\u7684 Gradient Estimation<\/strong>\u3002<\/p>\n\n\n\n
        8. \u591a\u4e2a Linac \u7684 Sequential Tuning<\/h2>\n\n\n\n
        \u5982\u679c\u6709 n \u4e2a Linac\uff0c\u5e76\u4e14\u6bcf\u4e2a Linac \u90fd\u6709 Phase \u548c Amplitude\uff0c\u90a3\u4e48\u4f18\u5316\u53c2\u6570\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n\n
        \u03b8 = {\u03c6\u2081, A\u2081, \u03c6\u2082, A\u2082, …, \u03c6\u2099, A\u2099}<\/strong><\/p>\n\n\n\n
        \u4e00\u4e2a\u6700\u7b80\u5355\u7684\u8c03\u8282\u7b56\u7565\u662f\u9010\u4e2a\u53c2\u6570\u8fdb\u884c\u4f18\u5316\uff1a<\/p>\n\n\n\n
        Phase\u2081\n   \u2193\n\u627e\u5230 Beam \u6700\u5927\u65b9\u5411\n   \u2193\n\u56fa\u5b9a\n\nPhase\u2082\n   \u2193\n\u627e\u5230 Beam \u6700\u5927\u65b9\u5411\n   \u2193\n\u56fa\u5b9a\n\nPhase\u2083\n   \u2193\n\u627e\u5230 Beam \u6700\u5927\u65b9\u5411\n   \u2193\n\u56fa\u5b9a\n\n...\n   \u2193\nPhase\u2099\n   \u2193\n\u518d\u4f18\u5316 Amplitude\n  <\/pre>\n\n\n\n
        \u8fd9\u5b9e\u9645\u4e0a\u975e\u5e38\u63a5\u8fd1\uff1a<\/p>\n\n\n\n
        Coordinate Descent<\/strong><\/p>\n\n\n\n
        \u6216\u8005\u5728\u7b80\u5355\u60c5\u51b5\u4e0b\u53ef\u4ee5\u7406\u89e3\u4e3a\uff1a<\/p>\n\n\n\n
        Hill Climbing<\/strong><\/p>\n\n\n\n
        9. \u4e3a\u4ec0\u4e48\u524d\u4e00\u7ea7 Linac \u4f1a\u5f71\u54cd\u540e\u4e00\u7ea7 Linac\uff1f<\/h2>\n\n\n\n
        \u8fd9\u662f\u591a\u7ea7 Linac \u7cfb\u7edf\u4e0e\u7b80\u5355\u7684\u72ec\u7acb\u53c2\u6570\u4f18\u5316\u6700\u5927\u7684\u533a\u522b\u4e4b\u4e00\u3002<\/p>\n\n\n\n
        \u5047\u8bbe\uff1a<\/p>\n\n\n\n
        Linac 1 \u2192 Linac 2 \u2192 Linac 3 \u2192 Linac 4\n  <\/pre>\n\n\n\n
        \u5982\u679c Linac 2 \u7684 Phase \u53d1\u751f\u53d8\u5316\uff0c\u5b83\u4e0d\u4ec5\u5f71\u54cd Linac 2 \u672c\u8eab\u7684 Energy Gain\uff0c\u8fd8\u53ef\u80fd\u6539\u53d8\uff1a<\/p>\n\n\n\n
          \n
        • Energy distribution<\/li>\n\n\n\n
        • Longitudinal phase space<\/li>\n\n\n\n
        • Phase acceptance<\/li>\n\n\n\n
        • Capture efficiency<\/li>\n\n\n\n
        • Downstream transmission<\/li>\n<\/ul>\n\n\n\n
          \u56e0\u6b64\u53ef\u80fd\u5f62\u6210\uff1a<\/p>\n\n\n\n
          Phase\u2082\n  \u2193\nEnergy \/ Phase Space\n  \u2193\nLinac 3 Capture\n  \u2193\nLinac 4 Transmission\n  \u2193\nFinal Beam\n  <\/pre>\n\n\n\n
          \u6240\u4ee5\u6700\u7ec8 Beam \u5bf9 Phase\u2082 \u7684\u54cd\u5e94\u5b9e\u9645\u4e0a\u5305\u542b\u4e86\u6574\u4e2a downstream system \u7684\u7efc\u5408\u5f71\u54cd\u3002<\/p>\n\n\n\n
          \u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48\u5b9e\u9645\u5de5\u7a0b\u5e08\u53ef\u4ee5\u5728\u6700\u540e\u4e00\u7ea7 Beam Diagnostics \u4e0a\u89c2\u5bdf\u7ed3\u679c\uff0c\u518d\u53cd\u8fc7\u6765\u51b3\u5b9a\u524d\u4e00\u7ea7 Linac \u5e94\u8be5\u5982\u4f55\u8c03\u6574\u3002<\/p>\n\n\n\n
          10. \u4ece Energy Optimization \u5230 Beam Count Optimization<\/h2>\n\n\n\n
          \u5982\u679c\u76ee\u6807\u53ea\u662f\u6700\u5927\u5316\u6700\u7ec8 Energy\uff0c\u90a3\u4e48\u95ee\u9898\u53ef\u4ee5\u7b80\u5316\u4e3a\uff1a<\/p>\n\n\n\n
          En<\/sub> = E0<\/sub> + \u03a3 ki<\/sub>Ai<\/sub>sin(\u03c6i<\/sub>)<\/strong><\/p>\n\n\n\n
          \u4f46\u662f\u5b9e\u9645 accelerator \u7684\u76ee\u6807\u901a\u5e38\u4e0d\u662f\u5355\u7eaf\u8ba9 Energy \u8d8a\u9ad8\u8d8a\u597d\u3002<\/p>\n\n\n\n
          \u66f4\u5b9e\u9645\u7684\u76ee\u6807\u53ef\u80fd\u662f\uff1a<\/p>\n\n\n\n
          J = Number of ions satisfying E \u2265 Etarget<\/sub><\/strong><\/p>\n\n\n\n
          \u4e5f\u5c31\u662f\u8bf4\u771f\u6b63\u9700\u8981\u4f18\u5316\u7684\u662f\uff1a<\/p>\n\n\n\n
          \u2202Nfinal<\/sub> \/ \u2202\u03c6i<\/sub><\/strong><\/p>\n\n\n\n
          \u800c\u4e0d\u662f\u7b80\u5355\u7684\uff1a<\/p>\n\n\n\n
          \u2202Efinal<\/sub> \/ \u2202\u03c6i<\/sub><\/strong><\/p>\n\n\n\n
          \u8fd9\u4e24\u4e2a\u95ee\u9898\u770b\u4f3c\u7c7b\u4f3c\uff0c\u4f46\u7269\u7406\u610f\u4e49\u5e76\u4e0d\u76f8\u540c\u3002 \u4e00\u4e2a Linac \u53ef\u80fd\u80fd\u591f\u63d0\u4f9b\u66f4\u9ad8\u7684 Energy Gain\uff0c\u5374\u56e0\u4e3a phase-space mismatch \u6216 downstream acceptance \u4e0b\u964d\u800c\u5bfc\u81f4\u6700\u7ec8\u6709\u6548 Beam Count \u51cf\u5c11\u3002<\/p>\n\n\n\n
          11. \u4ece\u4eba\u5de5\u8c03\u8282\u8d70\u5411 Automated Tuning<\/h2>\n\n\n\n
          \u5982\u679c\u628a\u76ee\u524d\u5de5\u7a0b\u5e08\u7684\u64cd\u4f5c\u8fc7\u7a0b\u62bd\u8c61\u51fa\u6765\uff0c\u53ef\u4ee5\u5f97\u5230\uff1a<\/p>\n\n\n\n
          \u8c03\u6574\u53c2\u6570\n   \u2193\n\u8fd0\u884c Accelerator\n   \u2193\nMeasure Beam\n   \u2193\n\u8ba1\u7b97 Objective\n   \u2193\n\u5224\u65ad\u53d8\u597d\u8fd8\u662f\u53d8\u574f\n   \u2193\n\u51b3\u5b9a\u4e0b\u4e00\u6b21\u8c03\u6574\u65b9\u5411\n   \u2193\n\u5faa\u73af\n  <\/pre>\n\n\n\n
          \u8fd9\u5df2\u7ecf\u53ef\u4ee5\u76f4\u63a5\u8f6c\u6362\u6210\u4e00\u4e2a\u81ea\u52a8\u4f18\u5316\u6846\u67b6\uff1a<\/p>\n\n\n\n
                       Accelerator\n                  \u2502\n                  \u25bc\n          Final Beam Diagnostics\n                  \u2502\n                  \u25bc\n             Objective J\n                  \u2502\n                  \u25bc\n          Gradient Estimator\n                  \u2502\n                  \u25bc\n        Phase \/ Amplitude Update\n                  \u2502\n                  \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n                                  \u2502\n                                  \u25bc\n                             Accelerator\n  <\/pre>\n\n\n\n
          \u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u4f7f\u7528\u591a\u79cd\u4f18\u5316\u7b97\u6cd5\uff0c\u5305\u62ec\uff1a<\/p>\n\n\n\n
            \n
          • Coordinate Descent<\/li>\n\n\n\n
          • Hill Climbing<\/li>\n\n\n\n
          • Finite Difference Optimization<\/li>\n\n\n\n
          • Nelder-Mead<\/li>\n\n\n\n
          • Bayesian Optimization<\/li>\n\n\n\n
          • SPSA\uff08Simultaneous Perturbation Stochastic Approximation\uff09<\/li>\n\n\n\n
          • Extremum Seeking<\/li>\n\n\n\n
          • Model Predictive Control<\/li>\n\n\n\n
          • Reinforcement Learning<\/li>\n<\/ul>\n\n\n\n
            12. SPSA \u4e0e\u4eba\u5de5 Phase Tuning \u7684\u7279\u6b8a\u76f8\u4f3c\u6027<\/h2>\n\n\n\n
            \u5f53 Linac \u6570\u91cf\u589e\u52a0\u4ee5\u540e\uff0c\u9010\u4e2a\u53c2\u6570\u8fdb\u884c \u00b1\u0394 \u626b\u63cf\u4f1a\u8d8a\u6765\u8d8a\u8017\u8d39 machine time\u3002<\/p>\n\n\n\n
            \u4f8b\u5982\u6709 50 \u4e2a Linac\uff0c\u6bcf\u4e2a Linac \u6709 Phase \u548c Amplitude\uff1a<\/p>\n\n\n\n
            Parameter Count = 50 \u00d7 2 = 100<\/strong><\/p>\n\n\n\n
            \u5982\u679c\u5bf9\u6bcf\u4e2a\u53c2\u6570\u5206\u522b\u8fdb\u884c\u6b63\u8d1f\u65b9\u5411\u6d4b\u8bd5\uff0c\u9700\u8981\u5927\u91cf machine shots\u3002<\/p>\n\n\n\n
            SPSA \u7684\u6838\u5fc3\u601d\u60f3\u5219\u662f\uff1a<\/p>\n\n\n\n
            \n
            \u540c\u65f6\u5bf9\u5927\u91cf\u53c2\u6570\u65bd\u52a0\u968f\u673a\u7684\u5c0f\u6270\u52a8\uff0c\u518d\u901a\u8fc7\u6700\u7ec8 Objective \u7684\u53d8\u5316\u4f30\u8ba1\u6574\u4e2a\u53c2\u6570\u7a7a\u95f4\u7684 Gradient Direction\u3002<\/p>\n<\/blockquote>\n\n\n\n
            \u8fd9\u4e0e\u5de5\u7a0b\u5e08\u73b0\u5728\u7684\u7ecf\u9a8c\u65b9\u6cd5\u5177\u6709\u975e\u5e38\u76f4\u63a5\u7684\u8054\u7cfb\uff1a<\/p>\n\n\n\n
            Phase\u2081  +\u0394\nPhase\u2082  -\u0394\nPhase\u2083  +\u0394\nPhase\u2084  +\u0394\n...\nAmplitude\u2099 -\u0394\n\n          \u2193\n\n      Accelerator\n\n          \u2193\n\n      Final Beam \u2191\n\n          \u2193\n\nEstimate Gradient Direction\n  <\/pre>\n\n\n\n
            \u56e0\u6b64\uff0c\u4ece\u201c\u4eba\u5de5\u7ecf\u9a8c\u8c03\u8282\u201d\u8fdb\u4e00\u6b65\u53d1\u5c55\u5230\u201c\u81ea\u52a8\u5316\u4f18\u5316\u201d\uff0c\u5e76\u4e0d\u9700\u8981\u5b8c\u5168\u6539\u53d8\u95ee\u9898\u672c\u8eab\u3002 \u53ea\u9700\u8981\u628a\u5de5\u7a0b\u5e08\u7684\u5224\u65ad\u8fc7\u7a0b\u6570\u5b66\u5316\u5373\u53ef\u3002<\/p>\n\n\n\n
            13. \u4e00\u4e2a\u7edf\u4e00\u7684\u6570\u5b66\u6846\u67b6<\/h2>\n\n\n\n
            \u7efc\u5408\u4ee5\u4e0a\u8ba8\u8bba\uff0c\u53ef\u4ee5\u5c06\u591a\u7ea7 Linac \u7cfb\u7edf\u5199\u6210\uff1a<\/p>\n\n\n\n
            Beami+1<\/sub> = fi<\/sub>( Beami<\/sub>, \u03c6i<\/sub>, Ai<\/sub> )<\/strong><\/p>\n\n\n\n
            \u540c\u65f6\uff0c\u5728\u7b80\u5316\u7684 accelerating model \u4e0b\uff1a<\/p>\n\n\n\n
            Ei+1<\/sub> = Ei<\/sub> + ki<\/sub>Ai<\/sub>sin(\u03c6i<\/sub>)<\/strong><\/p>\n\n\n\n
            \u6700\u7ec8\u5b9a\u4e49 Objective\uff1a<\/p>\n\n\n\n
            J(\u03b8) = Nfinal<\/sub>( E \u2265 Etarget<\/sub> )<\/strong><\/p>\n\n\n\n
            \u5176\u4e2d\uff1a<\/p>\n\n\n\n
            \u03b8 = {\u03c6\u2081, A\u2081, …, \u03c6\u2099, A\u2099}<\/strong><\/p>\n\n\n\n
            \u6700\u7ec8\u4f18\u5316\u95ee\u9898\u5c31\u662f\uff1a<\/p>\n\n\n\n
            maximize J(\u03b8)<\/strong><\/p>\n\n\n\n
            \u5982\u679c\u80fd\u591f\u5efa\u7acb\u5b8c\u6574\u7684 differentiable accelerator model\uff0c\u5219\u53ef\u4ee5\u8fdb\u4e00\u6b65\u8ba1\u7b97\uff1a<\/p>\n\n\n\n
            \u2207J(\u03b8) = [ \u2202J\/\u2202\u03c6\u2081, \u2202J\/\u2202A\u2081, …, \u2202J\/\u2202\u03c6\u2099, \u2202J\/\u2202A\u2099 ]<\/strong><\/p>\n\n\n\n
            \u6b64\u65f6\u5c31\u53ef\u4ee5\u771f\u6b63\u4f7f\u7528\u7c7b\u4f3c Gradient Descent \/ Gradient Ascent \u7684\u65b9\u6cd5\u8fdb\u884c\u4f18\u5316\u3002<\/p>\n\n\n\n
            14. \u7ed3\u8bba<\/h2>\n\n\n\n
            \u591a\u7ea7 Linac \u7684 Phase \/ Amplitude Tuning \u4e0e Neural Network Backpropagation \u4e4b\u95f4\u5b58\u5728\u4e00\u4e2a\u975e\u5e38\u6709\u610f\u4e49\u7684\u7ed3\u6784\u6027\u7c7b\u6bd4\u3002<\/p>\n\n\n\n
            \u4e24\u8005\u90fd\u5177\u6709\uff1a<\/p>\n\n\n\n
              \n
            • \u591a\u4e2a\u4e32\u8054\u7684 Stage\uff1b<\/li>\n\n\n\n
            • \u524d\u4e00\u7ea7\u7684\u72b6\u6001\u5f71\u54cd\u540e\u4e00\u7ea7\uff1b<\/li>\n\n\n\n
            • \u6700\u7ec8 Output \u51b3\u5b9a\u7cfb\u7edf\u662f\u5426\u8fbe\u5230\u76ee\u6807\uff1b<\/li>\n\n\n\n
            • \u53ef\u4ee5\u901a\u8fc7\u6700\u7ec8 Output \u7684\u53d8\u5316\u53cd\u5411\u5224\u65ad\u524d\u7ea7\u53c2\u6570\u7684\u4f18\u5316\u65b9\u5411\u3002<\/li>\n<\/ul>\n\n\n\n
              \u4f46\u662f\uff0c\u4e24\u8005\u4e0d\u80fd\u7b80\u5355\u5730\u8ba4\u4e3a\u662f\u540c\u4e00\u79cd\u7b97\u6cd5\u3002<\/p>\n\n\n\n
              Backpropagation \u662f\u57fa\u4e8e\u53ef\u5fae\u6570\u5b66\u6a21\u578b\u548c Chain Rule \u7684 Gradient Calculation\uff1b \u5b9e\u9645 Linac Tuning \u5219\u901a\u5e38\u662f\u5728\u771f\u5b9e\u673a\u5668\u4e0a\u901a\u8fc7 Beam Measurement \u8fdb\u884c Gradient Estimation\u3002<\/strong><\/p>\n\n\n\n
              \u56e0\u6b64\uff0c\u4e00\u4e2a\u66f4\u51c6\u786e\u7684\u63cf\u8ff0\u662f\uff1a<\/p>\n\n\n\n
              \n
              Multi-Linac tuning can be viewed as a black-box, gradient-based optimization problem, where machine measurements are used to estimate the sensitivity of the final beam to individual RF parameters.<\/strong><\/p>\n<\/blockquote>\n\n\n\n
              \u6362\u53e5\u8bdd\u8bf4\uff0c\u5de5\u7a0b\u5e08\u73b0\u573a\u6240\u505a\u7684\uff1a<\/p>\n\n\n\n
              \u201cPhase \u8c03\u5927\u4e00\u70b9\u201d\n       \u2193\n\u201cBeam \u53d8\u5927\u4e86\u201d\n       \u2193\n\u201c\u8bf4\u660e\u8fd9\u4e2a\u65b9\u5411\u662f\u5bf9\u7684\u201d\n       \u2193\n\u201c\u7ee7\u7eed\u5f80\u8fd9\u4e2a\u65b9\u5411\u8c03\u201d\n  <\/pre>\n\n\n\n
              \u4ece\u6570\u5b66\u89d2\u5ea6\u770b\uff0c\u672c\u8d28\u4e0a\u5df2\u7ecf\u662f\u5728\u8fdb\u884c\u4e00\u79cd\u975e\u5e38\u76f4\u89c2\u7684\uff1a<\/p>\n\n\n\n
              Gradient Sign Estimation\u3002<\/strong><\/p>\n\n\n\n
              \u800c\u5982\u679c\u8fdb\u4e00\u6b65\u628a\u8fd9\u4e2a\u8fc7\u7a0b\u81ea\u52a8\u5316\uff0c\u5c31\u53ef\u4ee5\u4ece\u4f20\u7edf\u7684\u4eba\u5de5 Tuning \u6f14\u5316\u4e3a\uff1a<\/p>\n\n\n\n
              Beam Diagnostics\n       \u2193\nObjective Function\n       \u2193\nGradient \/ Sensitivity Estimation\n       \u2193\nOptimization Algorithm\n       \u2193\nPhase \/ Amplitude Update\n       \u2193\nAccelerator\n       \u2193\nBeam Diagnostics\n       \u2193\n...\n  <\/pre>\n\n\n\n
              \u8fd9\u4e5f\u610f\u5473\u7740\uff0c\u591a\u7ea7 Linac Tuning \u4e0e\u73b0\u4ee3\u673a\u5668\u5b66\u4e60\u4f18\u5316\u7b97\u6cd5\u4e4b\u95f4\u5e76\u975e\u53ea\u662f\u4e00\u4e2a\u8868\u9762\u4e0a\u7684\u7c7b\u6bd4\uff0c\u800c\u662f\u53ef\u4ee5\u5efa\u7acb\u4e00\u4e2a\u76f8\u5f53\u660e\u786e\u7684\u6570\u5b66\u6865\u6881\u3002<\/p>\n\n\n\n
              \n\n\n\n
              \u6ce8\uff1a\u672c\u6587\u4e2d\u7684 \u0394E \u221d A sin(\u03c6) \u4e3a\u7b80\u5316\u6a21\u578b\u3002\u5b9e\u9645 RF accelerator \u4e2d\u7684 Energy Gain \u4ee5\u53ca Beam Transmission \u8fd8\u9700\u8981\u8003\u8651 synchronous phase\u3001RF field distribution\u3001transit-time factor\u3001phase-space acceptance\u3001space charge\u3001beam loading\u3001matching \u7b49\u56e0\u7d20\u3002\u5177\u4f53 Phase \u8868\u8fbe\u5f0f\u53d6 sin \u6216 cos \u53d6\u51b3\u4e8e\u7cfb\u7edf\u91c7\u7528\u7684 phase reference convention\u3002<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"
              \u591a\u7ea7 Linac \u8c03\u8c10\u4e0e\u53cd\u5411\u4f20\u64ad\u7b97\u6cd5\u7684\u7c7b\u6bd4\uff1a\u4ece P […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[89],"tags":[],"class_list":["post-3660","post","type-post","status-publish","format-standard","hentry","category-live"],"_links":{"self":[{"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/3660","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3660"}],"version-history":[{"count":4,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/3660\/revisions"}],"predecessor-version":[{"id":3666,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=\/wp\/v2\/posts\/3660\/revisions\/3666"}],"wp:attachment":[{"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3660"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.zengqq.com.cn\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}